|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+3 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0
\] |
[_Gegenbauer] |
✓ |
0.385 |
|
|
\[
{}\left (-2+x \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
0.487 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.421 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.597 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.071 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}x y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime \prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.422 |
|
|
\[
{}2 x \left (-1+x \right ) y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✓ |
0.707 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.601 |
|
|
\[
{}x y^{\prime \prime }+\left (2-2 x \right ) y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.688 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.586 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }-\left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.730 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
0.770 |
|
|
\[
{}4 x y^{\prime \prime }+y^{\prime }+8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.691 |
|
|
\[
{}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.583 |
|
|
\[
{}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.477 |
|
|
\[
{}3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.326 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{49}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.634 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.498 |
|
|
\[
{}y^{\prime \prime }+\left ({\mathrm e}^{-2 x}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.720 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (x^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+16 x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.483 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-6\right ) y = 0
\] |
[_Bessel] |
✓ |
0.656 |
|
|
\[
{}x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.163 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (36 x^{4}-16\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.562 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.225 |
|
|
\[
{}4 x y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.516 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+36 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.516 |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.295 |
|
|
\[
{}y^{\prime \prime }+k^{2} x^{4} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.292 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.389 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}\left (-1+x \right )^{2} y^{\prime \prime }-\left (-1+x \right ) y^{\prime }-35 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.415 |
|
|
\[
{}16 \left (x +1\right )^{2} y^{\prime \prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.389 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-5\right ) y = 0
\] |
[_Bessel] |
✓ |
0.682 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.690 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.646 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.491 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.048 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.404 |
|
|
\[
{}y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.535 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime }-\frac {y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.251 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.294 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.453 |
|
|
\[
{}y^{\prime }-6 y = 0
\] |
[_quadrature] |
✓ |
0.429 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.492 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.401 |
|
|
\[
{}9 y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.960 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.877 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.152 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.901 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.739 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.780 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.743 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.203 |
|
|
\[
{}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.947 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.555 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.240 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.928 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y}
\] |
[_separable] |
✓ |
2.125 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{y \left (x^{3}+1\right )}
\] |
[_separable] |
✓ |
1.873 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
1.938 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.479 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.295 |
|
|
\[
{}x y y^{\prime } = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
6.459 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}y^{\prime } = 3 y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
2.096 |
|
|
\[
{}x y^{\prime }+y = y^{2}
\] |
[_separable] |
✓ |
2.645 |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2} = 2
\] |
[_separable] |
✓ |
2.715 |
|
|
\[
{}y^{\prime }-x y^{2} = 2 x y
\] |
[_separable] |
✓ |
2.451 |
|
|
\[
{}\left (1+z^{\prime }\right ) {\mathrm e}^{-z} = 1
\] |
[_quadrature] |
✓ |
1.851 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+4 x +2}{2 y-2}
\] |
[_separable] |
✓ |
2.398 |
|
|
\[
{}{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.591 |
|
|
\[
{}\frac {y}{-1+x}+\frac {x y^{\prime }}{y+1} = 0
\] |
[_separable] |
✓ |
2.862 |
|
|
\[
{}x +2 x^{3}+\left (y+2 y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.790 |
|
|
\[
{}\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0
\] |
[_separable] |
✓ |
12.070 |
|
|
\[
{}\frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0
\] |
[_separable] |
✓ |
41.108 |
|
|
\[
{}2 x \sqrt {1-y^{2}}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.153 |
|