|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}}
\] |
[_separable] |
✓ |
2.171 |
|
|
\[
{}\sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2}
\] |
[_quadrature] |
✓ |
0.478 |
|
|
\[
{}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}}
\] |
[_separable] |
✓ |
2.272 |
|
|
\[
{}y^{\prime } = 1+\frac {2 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.403 |
|
|
\[
{}v^{\prime }+2 u v = 2 u
\] |
[_separable] |
✓ |
1.081 |
|
|
\[
{}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0
\] |
[_separable] |
✓ |
2.794 |
|
|
\[
{}u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1
\] |
[_separable] |
✓ |
2.445 |
|
|
\[
{}4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y+x^{3} = 16 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
120.153 |
|
|
\[
{}\theta ^{\prime \prime }-p^{2} \theta = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.634 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.466 |
|
|
\[
{}y^{\prime \prime }+12 y = 7 y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.342 |
|
|
\[
{}r^{\prime \prime }-a^{2} r = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.564 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.624 |
|
|
\[
{}y^{\prime \prime }+3 y = \sin \left (x \right )+\frac {\sin \left (3 x \right )}{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.188 |
|
|
\[
{}5 x^{\prime }+x = \sin \left (3 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.637 |
|
|
\[
{}x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime } = {\mathrm e}^{-3 t}
\] |
[[_high_order, _missing_y]] |
✓ |
0.150 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x = 17 x^{6}
\] |
[[_high_order, _missing_y]] |
✓ |
0.370 |
|
|
\[
{}t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 x^{\prime } t +16 x = \cos \left (3 \ln \left (t \right )\right )
\] |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.823 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = {\mathrm e}^{2 x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.607 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.437 |
|
|
\[
{}y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.002 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.199 |
|
|
\[
{}y^{\prime \prime } = -m^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.358 |
|
|
\[
{}1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.557 |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.538 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime } = x y
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.511 |
|
|
\[
{}y-2 y^{\prime } x -y {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.234 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.207 |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.697 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y = \frac {1}{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.547 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.510 |
|
|
\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.535 |
|
|
\[
{}y^{\prime \prime }-2 y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.980 |
|
|
\[
{}y^{\prime \prime }-{y^{\prime }}^{2}-y {y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.636 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.459 |
|
|
\[
{}y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.316 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.732 |
|
|
\[
{}y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 x y^{\prime } y+3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.896 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.619 |
|
|
\[
{}x^{3} v^{\prime \prime \prime }+2 x^{2} v^{\prime \prime }+v = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.201 |
|
|
\[
{}v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.740 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = -x^{2}+1
\] |
[_linear] |
✓ |
0.997 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \csc \left (x \right )^{2}
\] |
[_linear] |
✓ |
1.780 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.972 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x^{2} y = x^{3}-x^{2} \arctan \left (x \right )
\] |
[_linear] |
✗ |
3.604 |
|
|
\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.255 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}-1\right ) y = x^{3}
\] |
[_linear] |
✓ |
1.178 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.304 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
[_linear] |
✓ |
1.312 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = \sin \left (x \right ) y^{2}
\] |
[_separable] |
✓ |
2.672 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2}
\] |
[_separable] |
✓ |
3.088 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
5.205 |
|
|
\[
{}3 y^{2} y^{\prime }+y^{3} = x -1
\] |
[_rational, _Bernoulli] |
✓ |
2.093 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = y^{4} \sec \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.767 |
|
|
\[
{}y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.397 |
|
|
\[
{}\left (1+{\mathrm e}^{y}\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.143 |
|
|
\[
{}\sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.096 |
|
|
\[
{}y \left (3+y\right ) y^{\prime } = x \left (3+2 y\right )
\] |
[_separable] |
✓ |
2.276 |
|
|
\[
{}x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.673 |
|
|
\[
{}x^{3}+4 x y+y^{2}+\left (2 x^{2}+2 x y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.638 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.731 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.502 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
77.716 |
|
|
\[
{}5 x y^{\prime } y-x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.741 |
|
|
\[
{}\left (x^{2}+3 x y-y^{2}\right ) y^{\prime }-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.899 |
|
|
\[
{}\left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.769 |
|
|
\[
{}5 x y^{\prime } y-4 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
198.014 |
|
|
\[
{}\left (x^{2}-2 x y\right ) y^{\prime }+x^{2}-3 x y+2 y^{2} = 0
\] |
[_linear] |
✓ |
1.445 |
|
|
\[
{}3 x^{2} y^{\prime }+2 x^{2}-3 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.189 |
|
|
\[
{}\left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.107 |
|
|
\[
{}\left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.041 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.720 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 5 x -7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.970 |
|
|
\[
{}\left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.039 |
|
|
\[
{}\left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.116 |
|
|
\[
{}\left (2 x -2 y+5\right ) y^{\prime } = x -y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.003 |
|
|
\[
{}\left (6 x -4 y+1\right ) y^{\prime } = 3 x -2 y+1
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.047 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.323 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.402 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.420 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.133 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+2 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.562 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.560 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.559 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.480 |
|