|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.989 |
|
|
\[
{}e y^{\prime \prime } = -P \left (L -x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.864 |
|
|
\[
{}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.062 |
|
|
\[
{}e y^{\prime \prime } = P \left (-y+a \right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.285 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.309 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.073 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.283 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = \ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.107 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.883 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.623 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.205 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.194 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.427 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.280 |
|
|
\[
{}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.546 |
|
|
\[
{}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.262 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.194 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.907 |
|
|
\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.525 |
|
|
\[
{}y^{\prime \prime } = -a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.653 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
70.810 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.316 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.341 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.541 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 3 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.026 |
|
|
\[
{}x = y^{\prime \prime }+y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.867 |
|
|
\[
{}x = y+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.648 |
|
|
\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.400 |
|
|
\[
{}V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.457 |
|
|
\[
{}V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-3 z=0 \\ 7 y^{\prime }+63 y-36 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+2 y^{\prime }+3 y=0 \\ y^{\prime }+3 y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+z=0 \\ z^{\prime }+3 y+5 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+2 z=0 \\ z^{\prime }+2 y-4 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.603 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-3 y-2 z=0 \\ z^{\prime }+y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.787 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+z^{\prime }+6 y=0 \\ z^{\prime }+5 y+z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.603 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y^{\prime }+5 y-3 z=x +{\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y+3 z={\mathrm e}^{x} \\ y^{\prime }+3 y+4 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.558 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }-3 y+2 z={\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.799 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+5 y-2 z=x \\ y^{\prime }+4 y+z=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.852 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-9 z={\mathrm e}^{x} \\ y^{\prime }-y-3 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.338 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-2 y-2 z={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z={\mathrm e}^{4 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.135 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.412 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.199 |
|
|
\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.460 |
|
|
\[
{}y^{\prime \prime }-k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.639 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-y-1 = 0
\] |
[_separable] |
✓ |
2.039 |
|
|
\[
{}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
26.036 |
|
|
\[
{}y-x y^{\prime } = a \left (y^{2}+y^{\prime }\right )
\] |
[_separable] |
✓ |
1.572 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.404 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.178 |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
159.086 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
14.372 |
|
|
\[
{}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.510 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.487 |
|
|
\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.608 |
|
|
\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.441 |
|
|
\[
{}x +y y^{\prime }+\frac {-y+x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.894 |
|
|
\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.362 |
|
|
\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.874 |
|
|
\[
{}\left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
3.043 |
|
|
\[
{}y-x y^{\prime }+\ln \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.278 |
|
|
\[
{}\left (1+x y\right ) y-\left (1-x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.922 |
|
|
\[
{}a \left (x y^{\prime }+2 y\right ) = x y y^{\prime }
\] |
[_separable] |
✓ |
1.629 |
|
|
\[
{}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.411 |
|
|
\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.779 |
|
|
\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
35.381 |
|
|
\[
{}y \left (x y+2 y^{2} x^{2}\right )+x \left (x y-y^{2} x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.111 |
|
|
\[
{}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.566 |
|
|
\[
{}x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.822 |
|
|
\[
{}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
210.933 |
|
|
\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.520 |
|
|
\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
48.586 |
|
|
\[
{}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
9.108 |
|
|
\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.711 |
|
|
\[
{}x y^{\prime }-a y = x +1
\] |
[_linear] |
✓ |
1.651 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.263 |
|
|
\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
4.545 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = {\mathrm e}^{x} \left (x +1\right )^{n +1}
\] |
[_linear] |
✓ |
1.583 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\] |
[_linear] |
✓ |
1.392 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.783 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
6.125 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.309 |
|
|
\[
{}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\] |
[_rational, _Bernoulli] |
✓ |
3.138 |
|
|
\[
{}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.348 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.452 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.611 |
|
|
\[
{}-y+x y^{\prime } = x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.564 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
37.658 |
|
|
\[
{}\left (x^{2}-x^{2} y\right ) y^{\prime }+y^{2}+x y^{2} = 0
\] |
[_separable] |
✓ |
1.701 |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
[_linear] |
✓ |
1.876 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x +1} = \frac {x^{3}}{y^{2}}
\] |
[_rational, _Bernoulli] |
✓ |
2.440 |
|
|
\[
{}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.388 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
4.235 |
|
|
\[
{}x y^{\prime }+\frac {y^{2}}{x} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.449 |
|
|
\[
{}x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.990 |
|
|
\[
{}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\] |
[_linear] |
✓ |
2.449 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
14.848 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
1.230 |
|