| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 15201 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| 15202 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.620 |
|
| 15203 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+40 y^{\prime }+101 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-5\\ \end {array} \]
Using Laplace transform method. |
✗ |
✗ |
✗ |
✗ |
2.621 |
|
| 15204 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+34 y&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.621 |
|
| 15205 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+8 y^{\prime \prime }+16 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.623 |
|
| 15206 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.623 |
|
| 15207 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+13 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=6\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| 15208 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=-20\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| 15209 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=-24\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 15210 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=8\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| 15211 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=5\\ y^{\prime \prime \prime }\left (0\right )&=19\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.628 |
|
| 15212 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✗ |
✓ |
✓ |
2.628 |
|
| 15213 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+16 y^{\prime }+17 y&=17 t -1\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.628 |
|
| 15214 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t}\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.629 |
|
| 15215 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 t} t^{2}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| 15216 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&={\mathrm e}^{-2 t}\\ y \left (0\right )&=-{\frac {2}{13}}\\ y^{\prime }\left (0\right )&={\frac {1}{13}}\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 15217 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }-3 y^{\prime }+17 y&=17 t -1\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 15218 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.636 |
|
| 15219 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=t +2\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 15220 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }&={\mathrm e}^{-\frac {t}{2}}\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| 15221 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }+20 y&=\sin \left (2 t \right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| 15222 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2}\\ y \left (0\right )&=-12\\ y^{\prime }\left (0\right )&=7\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| 15223 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (t \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
2.639 |
|
| 15224 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&={\mathrm e}^{2 t}\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| 15225 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.639 |
|
| 15226 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✓ |
2.639 |
|
| 15227 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+y^{\prime }&=4 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (-2+t \right )\right )\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.641 |
|
| 15228 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.641 |
|
| 15229 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| 15230 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| 15231 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )\\ y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✗ |
✗ |
2.643 |
|
| 15232 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+13 y&=39 \operatorname {Heaviside}\left (t \right )-507 \left (-2+t \right ) \operatorname {Heaviside}\left (-2+t \right )\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.644 |
|
| 15233 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )\\ y \left (0\right )&={\frac {3}{4}}\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
2.645 |
|
| 15234 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 15235 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (-2+t \right )-\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=-{\frac {2}{3}}\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 15236 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .\\ y \left (0\right )&=-6\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 15237 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.646 |
|
| 15238 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.646 |
|
| 15239 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 15240 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 15241 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 \pi ^{2} y&=3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 15242 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=3 \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 15243 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.648 |
|
| 15244 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=1-\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 15245 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| 15246 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-7 y^{\prime }+6 y&=\delta \left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 15247 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 Q^{\prime }+100 Q&=\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (-2+t \right )\\ Q \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.650 |
|
| 15248 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y&=8\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ y^{\prime \prime }\left (0\right )&=-3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.650 |
|
| 15249 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=4\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 15250 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=3\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 15251 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=-t^{2}+2 t -10\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 15252 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
2.654 |
|
| 15253 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| 15254 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| 15255 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-6 y^{\prime } t +\sin \left (2 t \right ) y&=\ln \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| 15256 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.656 |
|
| 15257 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } t -y \ln \left (t \right )&=\cos \left (2 t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| 15258 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} y^{\prime \prime }-2 y^{\prime } t +y&=t^{4} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| 15259 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+y&=1 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.658 |
|
| 15260 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.658 |
|
| 15261 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.659 |
|
| 15262 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=5 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| 15263 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=3 t^{2} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| 15264 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| 15265 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )-4 y \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| 15266 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=\frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}\\ \frac {d}{d t}y \left (t \right )&=\frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| 15267 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-x+2 y&=0\\ y^{\prime }+y-x&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| 15268 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )+5 x \left (t \right )-2 y \left (t \right )&=0\\ 2 x \left (t \right )+\frac {d}{d t}y \left (t \right )-y \left (t \right )&=0\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
2.662 |
|
| 15269 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )-3 x \left (t \right )+2 y \left (t \right )&=0\\ \frac {d}{d t}y \left (t \right )-x \left (t \right )+3 y \left (t \right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.662 |
|
| 15270 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right )&=0\\ x \left (t \right )+y^{\prime }-y&=0\\ z^{\prime }\left (t \right )+x \left (t \right )+2 y-3 z \left (t \right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| 15271 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right )-\frac {z \left (t \right )}{2}\\ \frac {d}{d t}z \left (t \right )&=-2 x \left (t \right )+z \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| 15272 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )&=y \left (t \right )\\ \frac {d}{d t}x \left (t \right )-\frac {d}{d t}y \left (t \right )&=x \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.663 |
|
| 15273 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )+2 \frac {d}{d t}y \left (t \right )&=t\\ \frac {d}{d t}x \left (t \right )-\frac {d}{d t}y \left (t \right )&=x \left (t \right )+y \left (t \right )\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
2.664 |
|
| 15274 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }-y^{\prime }\left (t \right )&=x+y \left (t \right )-t\\ 2 x^{\prime }+3 y^{\prime }\left (t \right )&=2 x+6\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 15275 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \frac {d}{d t}x \left (t \right )-\frac {d}{d t}y \left (t \right )&=t\\ 3 \frac {d}{d t}x \left (t \right )+2 \frac {d}{d t}y \left (t \right )&=y \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.665 |
|
| 15276 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 \frac {d}{d t}x \left (t \right )-3 \frac {d}{d t}y \left (t \right )&=x \left (t \right )+y \left (t \right )\\ 3 \frac {d}{d t}x \left (t \right )-\frac {d}{d t}y \left (t \right )&=t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.665 |
|
| 15277 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right )&=0\\ 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right )&=y \left (t \right )+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| 15278 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )&=\sin \left (t \right )\\ x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| 15279 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t}\\ \frac {d}{d t}y \left (t \right )&=-5 x \left (t \right )+2 y \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| 15280 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t}\\ \frac {d}{d t}y \left (t \right )&=-12 x \left (t \right )+5 y \left (t \right )+37\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.668 |
|
| 15281 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t}\\ \frac {d}{d t}y \left (t \right )&=-10 x \left (t \right )+9 y \left (t \right )+37\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| 15282 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.669 |
|
| 15283 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=-x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| 15284 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t}\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t}\\ \frac {d}{d t}z \left (t \right )&=-x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.672 |
|
| 15285 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-2 x \left (t \right )+y \left (t \right )+2 z \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=-4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.672 |
|
| 15286 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t}\\ \frac {d}{d t}z \left (t \right )&=-2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| 15287 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }\left (t \right )&=7 x \left (t \right )+y-1-6 \,{\mathrm e}^{t}\\ y^{\prime }&=-4 x \left (t \right )+3 y+4 \,{\mathrm e}^{t}-3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 15288 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 15289 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t}\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 15290 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t}\\ \frac {d}{d t}y \left (t \right )&=-5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| 15291 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )-3 y \left (t \right )+z \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}\\ \frac {d}{d t}z \left (t \right )&=5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| 15292 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right )+z \left (t \right )-10 \cos \left (t \right )\\ \frac {d}{d t}z \left (t \right )&=x \left (t \right )+z \left (t \right )+2\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| 15293 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right )\\ \frac {d}{d t}z \left (t \right )&=-3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| 15294 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=-3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t}\\ \frac {d}{d t}y \left (t \right )&=4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t}\\ \frac {d}{d t}z \left (t \right )&=4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| 15295 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right )\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| 15296 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {d}{d t}x \left (t \right )&=9 x \left (t \right )-3 y \left (t \right )-6 t\\ \frac {d}{d t}y \left (t \right )&=-x \left (t \right )+11 y \left (t \right )+10 t\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
2.679 |
|
| 15297 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.680 |
|
| 15298 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }+y x&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| 15299 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-2 y^{\prime }+y^{\prime \prime }&=x^{{3}/{2}} {\mathrm e}^{x} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.684 |
|
| 15300 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=2 \sec \left (2 x \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
2.685 |
|