|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 y^{\prime } = \frac {1}{1+{\mathrm e}^{2 t}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.038 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
16.529 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.207 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.036 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.221 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.362 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.173 |
|
|
\[
{}y^{\prime \prime }-4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.253 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.910 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.394 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.654 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.356 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.074 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.348 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.318 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.419 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.085 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.491 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.900 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.011 |
|
|
\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.107 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.950 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.993 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.160 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.065 |
|
|
\[
{}5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.027 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
17.842 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.383 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.610 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.433 |
|
|
\[
{}3 x y^{\prime \prime }+11 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.729 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.563 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.397 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0
\] |
[_Jacobi] |
✓ |
0.646 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y^{\prime } y = 1
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.673 |
|
|
\[
{}4 x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.117 |
|
|
\[
{}9 x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
19.260 |
|
|
\[
{}x^{\prime \prime }+64 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
18.455 |
|
|
\[
{}x^{\prime \prime }+100 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
25.687 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
40.027 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.510 |
|
|
\[
{}x^{\prime \prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
24.383 |
|
|
\[
{}x^{\prime \prime }+256 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.528 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.217 |
|
|
\[
{}10 x^{\prime \prime }+\frac {x}{10} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
22.805 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.495 |
|
|
\[
{}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.204 |
|
|
\[
{}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.562 |
|
|
\[
{}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.976 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.534 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+20 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.674 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.081 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
8.891 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.530 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ -t +1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.933 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.128 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.218 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.879 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.969 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
79.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 \\ y^{\prime }=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.593 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2} \\ y^{\prime }={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.027 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1} \\ x_{2}^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.752 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+1 \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.749 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+6 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x-y \\ y^{\prime }=x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.631 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.667 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.765 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.806 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.805 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.118 |
|
|
\[
{}x^{\prime \prime }+16 x = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.164 |
|
|
\[
{}x^{\prime \prime }+x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.322 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.459 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
5.625 |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
9.945 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.706 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}-y}-x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
11.298 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
44.034 |
|
|
\[
{}y^{\prime } = \frac {y+1}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.468 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.391 |
|
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
1.957 |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.895 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.486 |
|
|
\[
{}x y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.425 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.392 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
1.597 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.298 |
|