| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25201 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.858 |
|
| 25202 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.861 |
|
| 25203 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=a\\ y^{\prime }\left (0\right )&=b\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.876 |
|
| 25204 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.905 |
|
| 25205 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
35.917 |
|
| 25206 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
35.925 |
|
| 25207 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
35.931 |
|
| 25208 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=-1\\ y^{\prime }\left (1\right )&=3\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.935 |
|
| 25209 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=a\\ y^{\prime }\left (1\right )&=b\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
35.958 |
|
| 25210 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t -4 y&=t^{4}\\ y \left (-1\right )&=y_{1}\\ y^{\prime }\left (-1\right )&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
35.996 |
|
| 25211 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1}\\ y \left (2\right )&=y_{1}\\ y^{\prime }\left (2\right )&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.003 |
|
| 25212 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right )\\ y \left (\frac {\pi }{2}\right )&=y_{1}\\ y^{\prime }\left (\frac {\pi }{2}\right )&=y_{1}\\ \end {array} \]
|
✗ |
✓ |
✗ |
✗ |
36.016 |
|
| 25213 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +t^{2} y&=\cos \left (t \right )\\ y \left (0\right )&=y_{1}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.020 |
|
| 25214 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0\\ y \left (10\right )&=y_{1}\\ y^{\prime }\left (10\right )&=y_{1}\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.020 |
|
| 25215 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t}\\ y \left (1\right )&=y_{1}\\ y^{\prime }\left (1\right )&=y_{1}\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
36.038 |
|
| 25216 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.038 |
|
| 25217 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.046 |
|
| 25218 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.067 |
|
| 25219 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.073 |
|
| 25220 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.075 |
|
| 25221 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.076 |
|
| 25222 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.081 |
|
| 25223 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.140 |
|
| 25224 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.181 |
|
| 25225 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -2 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.187 |
|
| 25226 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.201 |
|
| 25227 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t -21 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.213 |
|
| 25228 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +9 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.243 |
|
| 25229 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.273 |
|
| 25230 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -4 y&=0 \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
36.279 |
|
| 25231 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.311 |
|
| 25232 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.315 |
|
| 25233 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
36.384 |
|
| 25234 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
✓ |
✓ |
✗ |
✓ |
36.398 |
|
| 25235 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0\\ y \left (1\right )&=-3\\ y^{\prime }\left (1\right )&=4\\ \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.402 |
|
| 25236 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
36.404 |
|
| 25237 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.438 |
|
| 25238 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (1+t \right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.569 |
|
| 25239 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.582 |
|
| 25240 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.625 |
|
| 25241 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-4 y^{\prime }+t y&=0\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.630 |
|
| 25242 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.644 |
|
| 25243 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.654 |
|
| 25244 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.676 |
|
| 25245 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.704 |
|
| 25246 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
36.713 |
|
| 25247 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.717 |
|
| 25248 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
36.741 |
|
| 25249 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.760 |
|
| 25250 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
36.767 |
|
| 25251 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.773 |
|
| 25252 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
36.778 |
|
| 25253 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
36.800 |
|
| 25254 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=0 \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
36.829 |
|
| 25255 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.841 |
|
| 25256 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+4 y&=0 \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
36.846 |
|
| 25257 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.883 |
|
| 25258 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.911 |
|
| 25259 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.922 |
|
| 25260 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
36.933 |
|
| 25261 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
36.941 |
|
| 25262 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +\left (t^{2}+2\right ) y&=0 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
36.944 |
|
| 25263 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \end {array} \]
|
✓ |
✓ |
✗ |
✗ |
36.954 |
|
| 25264 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
36.957 |
|
| 25265 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.005 |
|
| 25266 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
37.027 |
|
| 25267 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
37.060 |
|
| 25268 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
37.072 |
|
| 25269 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \end {array} \]
|
✓ |
✓ |
✗ |
✓ |
37.074 |
|
| 25270 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
37.089 |
|
| 25271 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \end {array} \]
|
✗ |
✗ |
✗ |
✗ |
37.119 |
|
| 25272 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (t \right ) \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.129 |
|
| 25273 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
37.163 |
|
| 25274 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.197 |
|
| 25275 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.223 |
|
| 25276 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \end {array} \]
|
✗ |
✓ |
✓ |
✓ |
37.228 |
|
| 25277 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=t \end {array} \]
|
✓ |
✓ |
✓ |
✓ |
37.270 |
|
| 25278 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \end {array} \]
|
✗ |
✓ |
✓ |
✗ |
37.276 |
|
| 25279 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.310 |
|
| 25280 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{-t}} \end {array} \]
|
✓ |
✓ |
✓ |
✗ |
37.319 |
|
| 25281 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.320 |
|
| 25282 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
37.347 |
|
| 25283 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.355 |
|
| 25284 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
37.357 |
|
| 25285 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.367 |
|
| 25286 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.369 |
|
| 25287 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.372 |
|
| 25288 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.384 |
|
| 25289 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.388 |
|
| 25290 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .\\ y \left (\pi \right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.406 |
|
| 25291 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.427 |
|
| 25292 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.448 |
|
| 25293 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
37.480 |
|
| 25294 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.490 |
|
| 25295 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
37.504 |
|
| 25296 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.516 |
|
| 25297 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
37.532 |
|
| 25298 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right .\\ y \left (0\right )&=2\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.553 |
|
| 25299 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=-1\\ \end {array} \]
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
37.555 |
|
| 25300 |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Using Laplace transform method. |
✗ |
✓ |
✓ |
✗ |
37.586 |
|