|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.121 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.464 |
|
|
\[
{}y^{\prime \prime } = f \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.664 |
|
|
\[
{}y^{\prime \prime } = k
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
57.517 |
|
|
\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.301 |
|
|
\[
{}y^{\prime \prime } = 4 \sin \left (x \right )-4
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.467 |
|
|
\[
{}y y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.128 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.512 |
|
|
\[
{}y y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.120 |
|
|
\[
{}y^{2} y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.076 |
|
|
\[
{}y^{2} y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.126 |
|
|
\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.133 |
|
|
\[
{}3 y y^{\prime \prime }+y = 5
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
498.826 |
|
|
\[
{}a y y^{\prime \prime }+b y = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.974 |
|
|
\[
{}a y^{2} y^{\prime \prime }+b y^{2} = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.427 |
|
|
\[
{}a y y^{\prime \prime }+b y = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.597 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x+4 y \\ y^{\prime }=-6 x-y \\ z^{\prime }=6 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.284 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.282 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y \\ y^{\prime }=-4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z \\ y^{\prime }=-x+2 z \\ z^{\prime }=-x-2 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.337 |
|
|
\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
[_quadrature] |
✓ |
2.719 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.277 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.060 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
113.050 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
38.529 |
|
|
\[
{}y^{\prime } = -1+x^{2}+y^{2}
\] |
[_Riccati] |
✓ |
1.514 |
|
|
\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
[_Bernoulli] |
✓ |
1.230 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
68.110 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.719 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.028 |
|
|
\[
{}y^{\prime \prime }-y y^{\prime } = 2 x
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
4.686 |
|
|
\[
{}y^{\prime }-y^{2}-x -x^{2} = 0
\] |
[_Riccati] |
✓ |
4.658 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.084 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.047 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.073 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{2}-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.479 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{4}-6 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{5}+24 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.015 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.532 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.501 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.498 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.514 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.327 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{3}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.232 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.327 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.329 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.336 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{4}+3 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y x -x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime \prime }-y x -x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.901 |
|
|
\[
{}y^{\prime \prime }-y x -x^{6}+64 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.648 |
|
|
\[
{}y^{\prime \prime }-y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.394 |
|
|
\[
{}y^{\prime \prime }-y x -x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.809 |
|
|
\[
{}y^{\prime \prime }-y x -x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.532 |
|
|
\[
{}y^{\prime \prime }-y x -x^{6}-x^{3}+42 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.618 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.816 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
66.480 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.208 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.008 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.151 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
19.392 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
409.181 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.612 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.549 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x -y x -x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.862 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-y x -x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.650 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.573 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.560 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
131.480 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.063 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
395.854 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-y x -x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.546 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.552 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.565 |
|
|
\[
{}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.041 |
|
|
\[
{}y^{\prime \prime }+c y^{\prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.992 |
|
|
\[
{}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}
\] |
[_quadrature] |
✓ |
1.032 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.201 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.214 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.453 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.277 |
|