|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.507 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.497 |
|
|
\[
{}y^{\prime } = \frac {3 x -4 y-2}{3 x -4 y-3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.965 |
|
|
\[
{}x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
2.001 |
|
|
\[
{}y = x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.695 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x}+x^{3} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.136 |
|
|
\[
{}y \left (1+{y^{\prime }}^{2}\right ) = a
\] |
[_quadrature] |
✓ |
0.675 |
|
|
\[
{}x^{2}-y+\left (y^{2} x^{2}+x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.385 |
|
|
\[
{}3 y^{2}-x +2 y \left (y^{2}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.041 |
|
|
\[
{}\left (x -y\right ) y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.458 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{1-x +y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.398 |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.531 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.907 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.956 |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.227 |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.747 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.503 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.476 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.443 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.157 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+10 y = 100
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.341 |
|
|
\[
{}x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.148 |
|
|
\[
{}y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.049 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime \prime }+y = \cosh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.642 |
|
|
\[
{}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.299 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.394 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.832 |
|
|
\[
{}x^{3} x^{\prime \prime }+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.385 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.134 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
2.410 |
|
|
\[
{}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x]] |
✓ |
0.108 |
|
|
\[
{}x^{\prime \prime \prime \prime }-2 x^{\prime \prime }+x = t^{2}-3
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime }+4 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.240 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.823 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime } = 3 \sqrt {y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
8.026 |
|
|
\[
{}y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.126 |
|
|
\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.473 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.563 |
|
|
\[
{}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.671 |
|
|
\[
{}x^{\prime \prime }+9 x = t \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.080 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.684 |
|
|
\[
{}y^{\prime \prime \prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.520 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.135 |
|
|
\[
{}m x^{\prime \prime } = f \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.023 |
|
|
\[
{}m x^{\prime \prime } = f \left (x^{\prime }\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.532 |
|
|
\[
{}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.120 |
|
|
\[
{}x^{\prime \prime \prime \prime }+2 x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.794 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y = 2 \cos \left (\ln \left (x +1\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.780 |
|
|
\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.101 |
|
|
\[
{}x^{\prime \prime \prime \prime }+x = t^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.115 |
|
|
\[
{}{y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.514 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.692 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.246 |
|
|
\[
{}y^{\left (6\right )}-y = {\mathrm e}^{2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.146 |
|
|
\[
{}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.144 |
|
|
\[
{}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
0.473 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.336 |
|
|
\[
{}y^{\prime \prime } = 2 y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.402 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2} = y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.286 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x-3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.920 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.877 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x +y} \left (x^{2}+1\right )
\] |
[_separable] |
✓ |
1.756 |
|
|
\[
{}x^{2} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.074 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.530 |
|
|
\[
{}x \left ({\mathrm e}^{y}+4\right ) = {\mathrm e}^{x +y} y^{\prime }
\] |
[_separable] |
✓ |
2.408 |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.309 |
|
|
\[
{}x y^{\prime }+y = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.636 |
|
|
\[
{}y^{\prime } = t \ln \left (y^{2 t}\right )+t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.031 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{y^{2}-x}
\] |
[_separable] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = \ln \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.751 |
|
|
\[
{}x \left (y+1\right )^{2} = \left (x^{2}+1\right ) y \,{\mathrm e}^{y} y^{\prime }
\] |
[_separable] |
✓ |
2.384 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.755 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.040 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
6.104 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime } = 2 x^{2}+3
\] |
[[_high_order, _missing_y]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.039 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.040 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}} = \sinh \left (x \right )
\] |
[_linear] |
✓ |
37.188 |
|
|
\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
0.040 |
|
|
\[
{}y y^{\prime } = 1
\] |
[_quadrature] |
✓ |
1.965 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+3 y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.400 |
|
|
\[
{}5 y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
1.663 |
|
|
\[
{}{y^{\prime }}^{2} \sqrt {y} = \sin \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.607 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.538 |
|
|
\[
{}y^{\prime \prime \prime } = 1
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.089 |
|
|
\[
{}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.115 |
|
|
\[
{}y^{\prime \prime } = x^{2}+y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.045 |
|
|
\[
{}{y^{\prime }}^{2}+x y {y^{\prime }}^{2} = \ln \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
7.074 |
|
|
\[
{}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
0.051 |
|
|
\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\] |
[NONE] |
✗ |
0.288 |
|
|
\[
{}y^{\prime \prime } y = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.740 |
|
|
\[
{}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.081 |
|