|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.757 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.701 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.150 |
|
|
\[
{}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.037 |
|
|
\[
{}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.047 |
|
|
\[
{}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.069 |
|
|
\[
{}e y^{\prime \prime } = -P \left (L -x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.056 |
|
|
\[
{}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.174 |
|
|
\[
{}e y^{\prime \prime } = P \left (-y+a \right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.091 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x = \ln \left (x \right )^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.354 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.991 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.284 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = \ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.271 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.148 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.797 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.488 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.028 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \csc \left (x \right )^{2} = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.067 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.978 |
|
|
\[
{}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.398 |
|
|
\[
{}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
1.200 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.271 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.878 |
|
|
\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime } = -a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.424 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
77.857 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.491 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.571 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.709 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 3 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.036 |
|
|
\[
{}x = y^{\prime \prime }+y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.988 |
|
|
\[
{}x = {y^{\prime }}^{2}+y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.770 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.484 |
|
|
\[
{}V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.535 |
|
|
\[
{}V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.660 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-3 z=0 \\ 7 y^{\prime }+63 y-36 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.374 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+2 y^{\prime }+3 y=0 \\ y^{\prime }+3 y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+z=0 \\ z^{\prime }+3 y+5 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.313 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+2 z=0 \\ z^{\prime }+2 y-4 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.545 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-3 y-2 z=0 \\ z^{\prime }+y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.671 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+z^{\prime }+6 y=0 \\ z^{\prime }+5 y+z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y^{\prime }+5 y-3 z=x +{\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.918 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y+3 z={\mathrm e}^{x} \\ y^{\prime }+3 y+4 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.931 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }-3 y+2 z={\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.231 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+5 y-2 z=x \\ y^{\prime }+4 y+z=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.058 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-9 z={\mathrm e}^{x} \\ y^{\prime }-y-3 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.717 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-2 y-2 z={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z={\mathrm e}^{4 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.178 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.157 |
|
|
\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime }-k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.646 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
[_separable] |
✓ |
1.574 |
|
|
\[
{}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
33.732 |
|
|
\[
{}y-y^{\prime } x = a \left (y^{\prime }+y^{2}\right )
\] |
[_separable] |
✓ |
1.604 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.296 |
|
|
\[
{}x^{2}+y^{2}-2 x y^{\prime } y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.760 |
|
|
\[
{}y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.819 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
142.574 |
|
|
\[
{}\left (3 x +4 y\right ) y^{\prime }+y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
88.821 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.176 |
|
|
\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
88.627 |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.351 |
|
|
\[
{}x +y y^{\prime }+\frac {y^{\prime } x -y}{x^{2}+y^{2}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.526 |
|
|
\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.554 |
|
|
\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.551 |
|
|
\[
{}\left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 \,{\mathrm e}^{2 x} y-{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
3.029 |
|
|
\[
{}y-y^{\prime } x +\ln \left (x \right ) = 0
\] |
[_linear] |
✓ |
0.949 |
|
|
\[
{}\left (x y+1\right ) y-x \left (1-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.898 |
|
|
\[
{}a \left (y^{\prime } x +2 y\right ) = x y^{\prime } y
\] |
[_separable] |
✓ |
2.292 |
|
|
\[
{}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.589 |
|
|
\[
{}y \left ({\mathrm e}^{x}+2 x y\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.289 |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.739 |
|
|
\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.979 |
|
|
\[
{}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.240 |
|
|
\[
{}x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.889 |
|
|
\[
{}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.904 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.293 |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
46.452 |
|
|
\[
{}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.543 |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.321 |
|
|
\[
{}y^{\prime } x -a y = x +1
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.911 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
4.159 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = {\mathrm e}^{x} \left (x +1\right )^{n +1}
\] |
[_linear] |
✓ |
1.734 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\] |
[_linear] |
✓ |
1.194 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = y^{6} x^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.280 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
8.149 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.424 |
|
|
\[
{}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\] |
[_rational, _Bernoulli] |
✓ |
2.586 |
|
|
\[
{}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.482 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
12.497 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.200 |
|
|
\[
{}y^{\prime } x -y = x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.533 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
39.977 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.906 |
|
|
\[
{}y^{\prime }+\frac {\left (-2 x +1\right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
1.590 |
|