| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.443 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=a\\ y^{\prime }\left (0\right )&=b\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.248 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=-1\\ y^{\prime }\left (1\right )&=3\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=a\\ y^{\prime }\left (1\right )&=b\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t -4 y&=t^{4}\\ y \left (-1\right )&=y_{1}\\ y^{\prime }\left (-1\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
13.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1}\\ y \left (2\right )&=y_{1}\\ y^{\prime }\left (2\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.844 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right )\\ y \left (\frac {\pi }{2}\right )&=y_{1}\\ y^{\prime }\left (\frac {\pi }{2}\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
10.338 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +t^{2} y&=\cos \left (t \right )\\ y \left (0\right )&=y_{1}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
46.897 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0\\ y \left (10\right )&=y_{1}\\ y^{\prime }\left (10\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
16.163 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t}\\ y \left (1\right )&=y_{1}\\ y^{\prime }\left (1\right )&=y_{1}\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
34.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.228 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
35.482 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.588 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.307 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t -21 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.169 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.985 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.915 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0\\ y \left (1\right )&=-3\\ y^{\prime }\left (1\right )&=4\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✗ |
✗ |
✗ |
16.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
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. |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.032 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +\left (t^{2}+2\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
7.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.662 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.710 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=t \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
262.014 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{-t}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✓ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✗ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✓ |
✗ |
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. |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
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. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|