|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.604 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
1.308 |
|
|
\[
{}y^{\prime }+\sin \left (x \right ) y = y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.681 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
2.734 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
7.696 |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = x -1
\] |
[_rational, _Bernoulli] |
✓ |
2.054 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = y^{4} \sec \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.649 |
|
|
\[
{}y \sqrt {x^{2}-1}+x \sqrt {y^{2}-1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.656 |
|
|
\[
{}\left ({\mathrm e}^{y}+1\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.449 |
|
|
\[
{}\sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
8.545 |
|
|
\[
{}y \left (y+3\right ) y^{\prime } = x \left (3+2 y\right )
\] |
[_separable] |
✓ |
2.302 |
|
|
\[
{}x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.829 |
|
|
\[
{}x^{3}+4 x y+y^{2}+\left (2 x^{2}+2 x y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.934 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.166 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.816 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
941.839 |
|
|
\[
{}5 x y y^{\prime }-y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
233.014 |
|
|
\[
{}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.757 |
|
|
\[
{}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.752 |
|
|
\[
{}5 x y y^{\prime }-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
18.473 |
|
|
\[
{}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0
\] |
[_linear] |
✓ |
2.175 |
|
|
\[
{}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
3.753 |
|
|
\[
{}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.036 |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime } = 2 x -y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
55.519 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
16.971 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.198 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.527 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.424 |
|
|
\[
{}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.539 |
|
|
\[
{}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.563 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.734 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.959 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.103 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.205 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.355 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.629 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.743 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.612 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.566 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.236 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.132 |
|
|
\[
{}e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.012 |
|
|
\[
{}e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.095 |
|
|
\[
{}e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.099 |
|
|
\[
{}e y^{\prime \prime } = -P \left (L -x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.994 |
|
|
\[
{}e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.288 |
|
|
\[
{}e y^{\prime \prime } = P \left (-y+a \right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
622.984 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.678 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.178 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = \ln \left (x \right )
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.689 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.159 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.707 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.160 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.705 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.579 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.615 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
4.501 |
|
|
\[
{}\left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
5.605 |
|
|
\[
{}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
0.046 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.864 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.241 |
|
|
\[
{}x^{2} y^{\prime \prime } = \ln \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime } = -a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.352 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
714.540 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.927 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
19.293 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.904 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime } = 3 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.823 |
|
|
\[
{}x = y^{\prime \prime }+y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.556 |
|
|
\[
{}x = y+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.675 |
|
|
\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.893 |
|
|
\[
{}V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.880 |
|
|
\[
{}V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.080 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-3 z=0 \\ 7 y^{\prime }+63 y-36 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+2 y^{\prime }+3 y=0 \\ y^{\prime }+3 y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.611 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+z=0 \\ z^{\prime }+3 y+5 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+2 z=0 \\ z^{\prime }+2 y-4 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.729 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-3 y-2 z=0 \\ z^{\prime }+y-2 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.730 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+z^{\prime }+6 y=0 \\ z^{\prime }+5 y+z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.605 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y^{\prime }+5 y-3 z=x +{\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.889 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y+3 z={\mathrm e}^{x} \\ y^{\prime }+3 y+4 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.923 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }-3 y+2 z={\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{3 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.153 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+5 y-2 z=x \\ y^{\prime }+4 y+z=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.319 |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-9 z={\mathrm e}^{x} \\ y^{\prime }-y-3 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.750 |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-2 y-2 z={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z={\mathrm e}^{4 x} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.635 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.407 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.695 |
|