| # |
ODE |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=0\\ x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=0\\ x \left (0\right )&=3\\ x^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }-2 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+8 x^{\prime }+15 x&=0\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=\sin \left (2 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\cos \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=\cos \left (3 t \right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+3 x&=1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+2 x&=t\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+25 x&=0\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-6 x^{\prime }+8 x&=2\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x&=3 t\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+8 x&={\mathrm e}^{-t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }+x^{\prime \prime }-6 x^{\prime }&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ x^{\prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }-x&=0\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }+x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }+13 x^{\prime \prime }+36 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=-13\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }+8 x^{\prime \prime }+16 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x&={\mathrm e}^{2 t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+13 x&=t \,{\mathrm e}^{-t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=6 \cos \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }+\left (-2+t \right ) x^{\prime }+x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.371 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.370 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }-2 x^{\prime }+t x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x&=0\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+13 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\delta \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.157 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\delta \left (t \right )+\delta \left (t -\pi \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+4 x&=1+\delta \left (-2+t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+x&=t +\delta \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+2 x&=2 \delta \left (t -\pi \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+5 x&=\delta \left (t -\pi \right )+\delta \left (t -2 \pi \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+x&=\delta \left (t \right )-\delta \left (-2+t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+9 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }+8 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+8 x&=f \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\omega ^{2} y&=\cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t <\infty \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.892 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <3 \pi \\ 0 & 3 \pi \le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & \pi \le t <2 \pi \\ 0 & \operatorname {otherwise} \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.280 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.835 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=t^{2} \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+7 y&=\cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=t^{3}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (t_{0} \right )&=1\\ y^{\prime }\left (t_{0} \right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=t \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&={\mathrm e}^{t} t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+7 y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=1+{\mathrm e}^{-t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.164 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right .\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.036 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.801 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.356 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )+\delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=2 \delta \left (t -1\right )-\delta \left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}+3 \delta \left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=6 \,{\mathrm e}^{5 t}\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
49.781 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=8 \,{\mathrm e}^{3 t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=2 \,{\mathrm e}^{-t}\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=4 t\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=6 \cos \left (t \right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=5 \sin \left (2 t \right )\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=5 \,{\mathrm e}^{t} \sin \left (t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=0\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=4\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-12 y&=36\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=12\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=4 \,{\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=30 \,{\mathrm e}^{-3 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=10 \,{\mathrm e}^{-t}\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=12-6 \,{\mathrm e}^{t}\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=6 \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=13 \sin \left (2 t \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=8 \sin \left (t \right )-6 \cos \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=10 \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+4 y&=20 \sin \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=3 \cos \left (t \right )+\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=9 \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=6 \cos \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=7 \sin \left (4 t \right )+14 \cos \left (4 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&=A\\ y^{\prime }\left (0\right )&=B\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.200 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=\operatorname {Heaviside}\left (-2+t \right ) {\mathrm e}^{-2+t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.766 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )\\ y \left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=1-3 \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=-10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.147 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=5 \operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\delta \left (t -5\right )\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=\delta \left (-2+t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&=3 \delta \left (t -1\right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.234 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=\delta \left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=\delta \left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right )\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8 \sin \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (-2+t \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.205 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t}\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=15\\ y^{\prime }\left (0\right )&=-6\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \operatorname {Heaviside}\left (-2+t \right ) t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y&=\left (2 t^{2}+t +1\right ) \delta \left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=0\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=2\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&={\mathrm e}^{x}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\sin \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&={\mathrm e}^{x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.212 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=5\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} x^{2}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+4 x&=0\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2}\\ q \left (0\right )&=0\\ q^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {26 y}{5}&=\frac {97 \sin \left (2 t \right )}{5}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (0\right )&={\frac {3}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=0\\ y \left (0\right )&=11\\ y^{\prime }\left (0\right )&=28\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=10 \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y}{4}&=0\\ y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+5 y&=29 \cos \left (2 t \right )\\ y \left (0\right )&={\frac {16}{5}}\\ y^{\prime }\left (0\right )&={\frac {31}{5}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+7 y^{\prime }+12 y&=21 \,{\mathrm e}^{3 t}\\ y \left (0\right )&={\frac {7}{2}}\\ y^{\prime }\left (0\right )&=-10\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&={\frac {81}{10}}\\ y^{\prime }\left (0\right )&={\frac {39}{10}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+3 y&=6 t -8\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{25}&=\frac {t^{2}}{50}\\ y \left (0\right )&=-25\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}&=9 t^{3}+64\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&={\frac {63}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=0\\ y \left (4\right )&=-3\\ y^{\prime }\left (4\right )&=-17\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-6 y&=0\\ y \left (-1\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100\\ y \left (2\right )&=-4\\ y^{\prime }\left (2\right )&=14\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3}\\ y \left (\frac {3}{2}\right )&=4\\ y^{\prime }\left (\frac {3}{2}\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{\prime \prime }-6 y^{\prime }+y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+8 y&={\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+24 y&=144 t^{2}\\ y \left (0\right )&={\frac {19}{12}}\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=\left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.843 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .\\ y \left (\pi \right )&=1\\ y^{\prime }\left (\pi \right )&=2 \,{\mathrm e}^{-\pi }-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .\\ y \left (1\right )&=1+\cos \left (2\right )\\ y^{\prime }\left (1\right )&=4-2 \sin \left (2\right )\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=4 \delta \left (t -3 \pi \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.514 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.858 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=25 t -100 \delta \left (t -\pi \right )\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.643 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} L i^{\prime }+R i&=E_{0} \operatorname {Heaviside}\left (t \right )\\ i \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} L i^{\prime }+R i&=E_{0} \delta \left (t \right )\\ i \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} L i^{\prime }+R i&=E_{0} \sin \left (\omega t \right )\\ i \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-5 y&=1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-2 y&=-6 \,{\mathrm e}^{\pi -t}\\ y \left (\pi \right )&=1\\ y^{\prime }\left (\pi \right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.012 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-y&=t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+y&=3 \,{\mathrm e}^{-t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+3 y&=2 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+2 y&=t \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.780 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-7 y^{\prime }+12 y&={\mathrm e}^{2 t} t \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .\\ i \left (0\right )&=8\\ i^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
23.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=1\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }&=0\\ y \left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+6 y&={\mathrm e}^{4 t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
29.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=2 \cos \left (5 t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }&=6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sqrt {2}\, \sin \left (\sqrt {2}\, t \right )\\ y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.405 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (3 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.547 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&={\mathrm e}^{-3 t} \cos \left (2 t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.762 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&={\mathrm e}^{-4 t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
30.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=1+{\mathrm e}^{t} t\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+13 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&={\mathrm e}^{t} \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=1+t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+20 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (\pi \right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.006 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.533 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=\operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
11.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=1-\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=t \sin \left (t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=t \,{\mathrm e}^{t} \sin \left (t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.844 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\cos \left (3 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right )+t \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\delta \left (t -1\right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.275 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=1+\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+10 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2}\\ y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=t\\ y \left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-t y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
0.757 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=0\\ y \left (x_{0} \right )&=y_{0}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=0\\ y \left (1\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=\sin \left (t \right )\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
1.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=t\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } t +y&=t\\ y \left (1\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y+y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a t +1\right ) y^{\prime }+y&=t\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.723 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\left (a t +b t \right ) y&=0\\ y \left (-3\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+5 x&=\operatorname {Heaviside}\left (-2+t \right )\\ x \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=\sin \left (2 t \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }-6 x&=0\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+2 x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+2 x&={\mathrm e}^{-t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }&=0\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=\sin \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x&=1\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+\operatorname {Heaviside}\left (t -1\right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 \operatorname {Heaviside}\left (t -1\right )\\ x \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=-x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ x \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.778 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+\pi ^{2} x&=\pi ^{2} \operatorname {Heaviside}\left (1-t \right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x&=1-\operatorname {Heaviside}\left (t -1\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-4 t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x&=\delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right )\\ x \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x&=\delta \left (t -5\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=\delta \left (-2+t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\delta \left (-2+t \right )-\delta \left (t -5\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.430 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=3 \delta \left (t -2 \pi \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=\frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{3 t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=2 \sin \left (t \right )\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-12 y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=10\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.007 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+5 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=0\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+5 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+37 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=\frac {\sqrt {2}}{2}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-20 y^{\prime }+51 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-14\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+3 y^{\prime }+y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.512 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+34 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=-20\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=-24\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=5\\ y^{\prime \prime \prime }\left (0\right )&=19\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&={\mathrm e}^{-2 t}\\ y \left (0\right )&=-{\frac {2}{13}}\\ y^{\prime }\left (0\right )&={\frac {1}{13}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.824 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=t +2\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.278 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}}\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2}\\ y \left (0\right )&=-12\\ y^{\prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.152 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.258 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&={\frac {3}{4}}\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=-{\frac {2}{3}}\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .\\ y \left (0\right )&=-6\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.031 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.236 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
12.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.958 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ Q \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.037 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ y^{\prime \prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=18 t\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+3 y&=f \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right .\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 t x^{\prime }-4 x&=1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.311 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (t -1\right )-\delta \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=4 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x}\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&=2 \,{\mathrm e}^{x}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=2+x\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=2+x\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=-x^{2}+1\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=x +\cos \left (x \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-2 y&=6\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&={\mathrm e}^{x}\\ y \left (0\right )&={\frac {5}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.923 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.785 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=18 \,{\mathrm e}^{3 x}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}\\ y \left (0\right )&={\frac {11}{4}}\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \sin \left (x \right )\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
18.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
9.972 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+3 y&=\delta \left (x -2\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (x -2\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\delta \left (x -\pi \right )+\delta \left (x -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \delta \left (-1+x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=\cos \left (x \right )+2 \delta \left (x -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\cos \left (x \right ) \delta \left (x -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.880 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8\\ y \left (0\right )&=11\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&={\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+13 y&=13 \operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\cos \left (2 t \right )\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+9 y&=20 \operatorname {Heaviside}\left (-2+t \right ) \sin \left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
3.483 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.857 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y&=5 \delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -3\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=-2 \delta \left (-2+t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=\delta \left (t -1\right )-3 \delta \left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.825 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&={\mathrm e}^{-2 t} \sin \left (4 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+5 y&=\operatorname {Heaviside}\left (-2+t \right ) \sin \left (-8+4 t \right )\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+3 y&=\left (1-\operatorname {Heaviside}\left (-2+t \right )\right ) {\mathrm e}^{\frac {1}{5}-\frac {t}{10}} \sin \left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
3.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.500 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=t\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&=0\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=t^{3}\\ y \left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=t^{3}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=12\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (2 t \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.012 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=7\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+y^{\prime }+t y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=9\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=27 t^{3}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.810 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t}\\ y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+17 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=12\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&=t^{2} {\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+13 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+17 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-12\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t}\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.807 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&={\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&=1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{-3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 \delta \left (-2+t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\delta \left (-2+t \right )-\delta \left (t -4\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\delta \left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\delta \left (t -1\right )-\delta \left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=4 \delta \left (t -1\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t \right )+\delta \left (t -\pi \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=-2 \delta \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\delta \left (-2+t \right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.649 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-16 y&=\delta \left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=\delta \left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-12 y^{\prime }+45 y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+9 y^{\prime }&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x&={\mathrm e}^{-2 t}\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1\\ x \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t}\\ x \left (0\right )&=-{\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=2 \sin \left (t \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=\cos \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x^{\prime }&=0\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }&=1\\ x \left (0\right )&=-1\\ x^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=t\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }&=12 t +2\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+2 x&=2\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+4 x&=4\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime \prime }-2 x^{\prime }&=\left (1+t \right ) {\mathrm e}^{t}\\ x \left (0\right )&={\frac {1}{2}}\\ x^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=2 \cos \left (t \right )\\ x \left (0\right )&=-1\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-2 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{\prime \prime }+5 y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=t^{2} {\mathrm e}^{t}+7\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }-6 y&=t^{2}+7\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=t \cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.633 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y&=t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=9\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=9\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
7.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-12 y&=0\\ y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=t\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+25 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+29 y&={\mathrm e}^{-2 t} \sin \left (5 t \right )\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=\cos \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=18 \,{\mathrm e}^{-t}\\ y \left (0\right )&=7\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-9 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-3\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right .\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (t \right )-\sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.304 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.956 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -3 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} \frac {t}{2} & 0\le t <6 \\ 3 & 6\le t \end {array}\right .\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
1.907 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=12\\ y^{\prime }\left (0\right )&=7\\ y^{\prime \prime }\left (0\right )&=2\\ y^{\prime \prime \prime }\left (0\right )&=-9\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=1-\operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2}\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.348 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=2 \left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )\\ u \left (0\right )&=0\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\delta \left (t -\pi \right )+\operatorname {Heaviside}\left (t -10\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=-20 \delta \left (t -3\right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=\sin \left (t \right )+\delta \left (t -3 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -4 \pi \right )\\ y \left (0\right )&={\frac {1}{2}}\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.482 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -2 \pi \right ) \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 \delta \left (t -\frac {\pi }{4}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )+3 \delta \left (t -\frac {3 \pi }{2}\right )-\operatorname {Heaviside}\left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{6}\right ) \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=\cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{2}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{4}+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{5}+y&=k \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+w^{2} y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+25 y&=\sin \left (\alpha t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+17 y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (\alpha t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=g \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {7 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {8 y^{\prime \prime }}{5}+y&=\operatorname {Heaviside}\left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=3 \,{\mathrm e}^{2 x}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=2\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }&=3 x^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sin \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=\operatorname {yd}_{0}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y&=0\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=\operatorname {yd}_{0}\\ \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
8.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (x \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }&=t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.962 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&={\mathrm e}^{2 t} t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-4 y&=t^{2}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-2 y&={\mathrm e}^{t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -1\right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+18 y&=2 \operatorname {Heaviside}\left (\pi -t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&={\mathrm e}^{t}\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=t\\ x \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+x&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x^{\prime }+3 x&=1\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }+x^{\prime \prime }&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ x^{\prime \prime }\left (0\right )&=0\\ x^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x&=\operatorname {Heaviside}\left (t -a \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
45.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=\operatorname {Heaviside}\left (t -a \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
15.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x&=k \delta \left (t \right )\\ x \left (0\right )&=a\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=g \left (t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=\delta \left (-t +a \right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (\pi \right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&={\mathrm e}^{5 t}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=t\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&={\mathrm e}^{5 t}\\ y \left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\sin \left (t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\cos \left (t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+b y&=1\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=t\\ y \left (0\right )&=-3\\ y \left (1\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 t & 0\le t \le 1 \\ 4 & 1<t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
11.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=10 \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&=0\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=0\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+n^{2} y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=k\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{-t}\\ y \left (0\right )&={\frac {3}{2}}\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=5 \cos \left (2 t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0\\ y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=8\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-3\\ y^{\prime \prime \prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=-4\\ y^{\prime \prime \prime }\left (0\right )&=12\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=t \sin \left (t \right )\\ y \left (0\right )&={\frac {7}{9}}\\ y^{\prime }\left (0\right )&=-{\frac {5}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=2 t -8\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=2 \cos \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&={\mathrm e}^{5 x}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
17.827 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-5 y&=0\\ y \left (\pi \right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\sin \left (x \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+4 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=4 t^{2}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & t <1 \\ 2 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
0.884 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=2\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&={\mathrm e}^{t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (1\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+5 y&=0\\ y \left (1\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&={\mathrm e}^{t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=\sin \left (t \right )\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (\pi \right )&=0\\ y^{\prime }\left (\pi \right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.578 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=5\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+3 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=4\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=12 t\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+25 y&=100\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=20\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=\cos \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (0\right )&=0\\ y \left (\frac {\pi }{2}\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime } t +y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=5 \delta \left (t -1\right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=3 \delta \left (t -\pi \right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=0\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=4 \cos \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }-4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=13 \cos \left (2 t \right )\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=6 \,{\mathrm e}^{t}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=-3 \,{\mathrm e}^{t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+25 y&=2 \,{\mathrm e}^{-5 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-27 y&=0\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=6\\ y^{\prime \prime }\left (0\right )&=18\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y^{\prime }+18 y&=54\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=20 \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=18\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&={\mathrm e}^{t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.943 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+26 y&=37 \,{\mathrm e}^{t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=-1\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.803 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y&=-1\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=2 \,{\mathrm e}^{t}\\ y \left (1\right )&={\mathrm e}^{3}-{\mathrm e}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=27 t\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.915 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-4 y&=25 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+13 y^{\prime }+36 y&=10-72 t\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-9\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.926 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-10 y^{\prime }+21 y&=21 t^{2}+t +13\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=11\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y&=12 \sinh \left (t \right )\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=39 \,{\mathrm e}^{t} \sin \left (t \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t}+5 t\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y&=18 \,{\mathrm e}^{2 t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=13\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+8 y&=-12 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=-8\\ y^{\prime }\left (0\right )&=24\\ y^{\prime \prime }\left (0\right )&=-46\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=2 t^{2}+2 \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=13 t +17+40 \sin \left (t \right )\\ y \left (0\right )&=30\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x \sin \left (x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=3 x -6\\ y \left (0\right )&={\frac {1}{3}}\\ y^{\prime }\left (0\right )&={\frac {4}{3}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=2 x\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-{\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}&=120\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=6\\ y^{\prime \prime \prime \prime }\left (0\right )&=24\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+y&={\mathrm e}^{x}\\ y \left (2\right )&=\frac {4 \,{\mathrm e}^{2}}{3}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=x^{2}\\ y \left (\frac {\pi }{2}\right )&=\frac {\pi ^{2}}{4}\\ y^{\prime }\left (\frac {\pi }{2}\right )&=2 \pi \\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=0\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=1\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&={\mathrm e}^{4 t}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
65.130 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+a y&={\mathrm e}^{-a t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=3 \,{\mathrm e}^{t}\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+25 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=0\\ y \left (0\right )&=y_{0}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+16 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=4 \,{\mathrm e}^{2 t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.420 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{-2 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=8\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=9 \,{\mathrm e}^{2 t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-5 y&=150 t\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=4\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t}\\ y \left (0\right )&=-3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=4 \cos \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\sin \left (3 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \cos \left (t \right )+\sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=4 \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=36 t \sin \left (3 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y&=4 t^{2} \cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=32 t \cos \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.371 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (1+t \right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-4 y^{\prime }+t y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.343 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.486 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.509 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
2.047 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
0.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
5.854 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
1.827 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .\\ y \left (\pi \right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✗ |
0.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
9.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.324 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.850 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
6.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right .\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
9.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
7.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
4.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.232 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=3+\delta \left (-2+t \right )\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.887 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=\delta \left (t -4\right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\delta \left (t -1\right )-\delta \left (t -3\right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.719 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=2 \delta \left (-2+t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+4 y&=3 \delta \left (t -1\right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=3 \delta \left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
5.950 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&=\delta \left (t -3\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\delta \left (t -1\right )-\delta \left (-2+t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&=\delta \left (t -3\right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=0\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+16 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+16 y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
4.683 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{a t}\\ y \left (0\right )&=A\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
222.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&={\mathrm e}^{a t}\\ y \left (0\right )&=A\\ y^{\prime }\left (0\right )&=B\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }&=1\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (\omega t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
3.861 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\cos \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-a y&=t\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=1\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=1\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.371 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\delta \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+B y^{\prime }+C y&=\delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+B y^{\prime }+C y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\sin \left (t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\sin \left (t \right )+\delta \left (t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{3 t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.364 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=12\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }&=8 t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=4 t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=2 \,{\mathrm e}^{-t} \cos \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+3 x&={\mathrm e}^{-2 t}\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1\\ x \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+x&=2 \sin \left (t \right )\\ x \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t}\\ x \left (0\right )&=-{\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+3 x&=1\\ x \left (0\right )&=3\\ x^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+2 x&=1\\ x \left (0\right )&={\frac {1}{2}}\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-5 x^{\prime }+6 x&=12\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }-1&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&={\frac {1}{3}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+1&=0\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+2 x&=2 t^{2}+1\\ x \left (0\right )&=4\\ x^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }-3 x&=3 t^{2}+7 t +3\\ x \left (0\right )&=-1\\ x^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-7 x^{\prime }&=-14 t -5\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }&=6 t^{2}+6 t -3\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-{\frac {3}{2}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+6 x^{\prime }&=t\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-{\frac {1}{36}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+x&=2 \,{\mathrm e}^{t}\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 7 x^{\prime \prime }+14 x^{\prime }&=\left (t -\frac {1}{4}\right ) {\mathrm e}^{-2 t}\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-{\frac {1}{56}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x^{\prime }+4 x&=\left (t -1\right ) {\mathrm e}^{2 t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{\prime \prime }-4 x^{\prime }+x&={\mathrm e}^{\frac {t}{2}}\\ x \left (0\right )&=-2\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-t}+{\mathrm e}^{-2 t}\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }-6 x&=6 \,{\mathrm e}^{3 t}+2 \,{\mathrm e}^{-2 t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&={\frac {4}{5}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }+4 x&=t^{2} {\mathrm e}^{-2 t}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-x^{\prime }&=2 \sin \left (t \right )\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+9 x&=18 \cos \left (3 t \right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=9\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2}\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&={\frac {1}{8}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+2 x^{\prime }+3 x&=t \cos \left (t \right )\\ x \left (0\right )&=-{\frac {1}{4}}\\ x^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-2 x^{\prime }+10 x&=\cos \left (3 t \right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&={\frac {18}{37}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-4 x^{\prime }+5 x&=2 \,{\mathrm e}^{2 t} \left (\sin \left (t \right )+\cos \left (t \right )\right )\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }-x^{\prime \prime }&=0\\ x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=3\\ x^{\prime \prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }-x&=2\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=\frac {1}{2}+\frac {\sqrt {3}}{2}\\ x^{\prime \prime }\left (0\right )&=\frac {1}{2}-\frac {\sqrt {3}}{2}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }+x^{\prime \prime }-2 x&={\mathrm e}^{t} t\\ x \left (0\right )&=2\\ x^{\prime }\left (0\right )&={\frac {21}{25}}\\ x^{\prime \prime }\left (0\right )&=-{\frac {28}{25}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.781 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (t +\frac {\pi }{4}\right )\\ x \left (0\right )&=-{\frac {40}{17}}\\ x^{\prime }\left (0\right )&={\frac {24}{17}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (2 t +\frac {\pi }{4}\right )\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&=1\\ y \left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-9 y&=t\\ y \left (0\right )&=5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y&=\cos \left (t \right )\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&={\mathrm e}^{-t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=1-t\\ y \left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=1\\ y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\cos \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=t^{2}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y&=1+t\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 3 & 4\le t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 12 & 4\le t \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.216 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-8 y&=\left \{\begin {array}{cc} 0 & 0\le t <6 \\ 2 & 6\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} -2 & 0\le t <3 \\ 0 & 3\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.226 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 2 & 5\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <3 \\ t +2 & 3\le t \end {array}\right .\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-5 y^{\prime }+6 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime }+12 y&=f \left (t \right )\\ y \left (0\right )&=-3\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-5 y&=f \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=f \left (t \right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-k^{2} y&=f \left (t \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-11 y^{\prime \prime }+18 y&=f \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=3 \delta \left (-2+t \right )-4 \delta \left (t -5\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=6 \delta \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+16 y^{\prime }&=12 \delta \left (t -\frac {5 \pi }{8}\right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime }-2 y&=2 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.116 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime } t -4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-16 y^{\prime } t +32 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.328 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime } t -8 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }+y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime } t -4 y&=6\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.430 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime } t&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime } t +4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=10\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-8 y^{\prime } t +16 y&=3\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.400 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&=2\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=60 \,{\mathrm e}^{t} \sin \left (2 t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=12 \,{\mathrm e}^{t} t\\ y \left (0\right )&={\frac {1}{2}}\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&={\frac {1}{2}}\\ y^{\prime \prime \prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.381 |
|