|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.881 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.161 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (x +1\right )^{2}}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.833 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.735 |
|
|
\[
{}y^{\prime }+4 y = 0
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}y^{\prime }-2 y = t^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.479 |
|
|
\[
{}y^{\prime }+3 y = \operatorname {Heaviside}\left (-4+t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime }-4 y = t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.376 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.412 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.343 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 7
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.684 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime }+9 y = 27 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.362 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+17 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.346 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.376 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.530 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.460 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.397 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.261 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.223 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.366 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.403 |
|
|
\[
{}y^{\prime } = \operatorname {Heaviside}\left (t -3\right )
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.668 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[_quadrature] |
✓ |
0.566 |
|
|
\[
{}y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.457 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.803 |
|
|
\[
{}y^{\prime } = 3 \delta \left (t -2\right )
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}y^{\prime } = \delta \left (t -2\right )-\delta \left (-4+t \right )
\] |
[_quadrature] |
✓ |
0.529 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -3\right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (-4+t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime }+2 y = 4 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.594 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.367 |
|
|
\[
{}y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.560 |
|
|
\[
{}y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.182 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }-16 y = \delta \left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.279 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.065 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (-4+t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
3.760 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.428 |
|
|
\[
{}y^{\prime }-2 y = 0
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.424 |
|
|
\[
{}y^{\prime }+\frac {2 y}{2 x -1} = 0
\] |
[_separable] |
✓ |
0.453 |
|
|
\[
{}\left (x -3\right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.352 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.431 |
|
|
\[
{}y^{\prime }+\frac {y}{-1+x} = 0
\] |
[_separable] |
✓ |
0.394 |
|
|
\[
{}y^{\prime }+\frac {y}{-1+x} = 0
\] |
[_separable] |
✓ |
0.485 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-2 y = 0
\] |
[_separable] |
✓ |
0.477 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.469 |
|
|
\[
{}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
0.382 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
0.500 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
0.497 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.377 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.360 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.357 |
|
|
\[
{}y^{\prime \prime }-3 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.315 |
|
|
\[
{}\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.434 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.357 |
|
|
\[
{}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.678 |
|
|
\[
{}y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.393 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.439 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.393 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.484 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0
\] |
[_Gegenbauer] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.446 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.408 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.640 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.153 |
|