|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.014 |
|
|
\[
{}x^{2} \left (2-x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.331 |
|
|
\[
{}3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.345 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}x^{2} y^{\prime }-x y = \frac {1}{x}
\] |
[_linear] |
✓ |
1.296 |
|
|
\[
{}x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.571 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}r^{\prime \prime }-6 r^{\prime }+9 r = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.840 |
|
|
\[
{}2 x -y \sin \left (2 x \right ) = \left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime }
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.415 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.559 |
|
|
\[
{}3 x^{3} y^{2} y^{\prime }-y^{3} x^{2} = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.670 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.758 |
|
|
\[
{}y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.368 |
|
|
\[
{}u \left (-v +1\right )+v^{2} \left (1-u\right ) u^{\prime } = 0
\] |
[_separable] |
✓ |
1.450 |
|
|
\[
{}y+2 x -x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.240 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 4 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.085 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 26 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.002 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.455 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 6 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.043 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.000 |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }-x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.949 |
|
|
\[
{}\left (x \cos \left (y\right )-{\mathrm e}^{-\sin \left (y\right )}\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.073 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime }+\sin \left (x \right )^{2}+\left (x +y\right ) \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
4.275 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 5 x +4 \,{\mathrm e}^{x} \left (1+\sin \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.241 |
|
|
\[
{}y^{\prime }+x y = \frac {x}{y}
\] |
[_separable] |
✓ |
1.568 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2}
\] |
[_linear] |
✓ |
2.898 |
|
|
\[
{}x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y^{\prime } y
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.757 |
|
|
\[
{}3 x^{2} y+x^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.172 |
|
|
\[
{}-y+x y^{\prime } = x^{2}
\] |
[_linear] |
✓ |
1.487 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.557 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.838 |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
0.487 |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
1.111 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
0.560 |
|
|
\[
{}y^{\prime } = 3 x^{2} y
\] |
[_separable] |
✓ |
1.175 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
0.427 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.220 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime } = -4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.983 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.945 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.844 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.777 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.243 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.942 |
|
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.148 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.465 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.216 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.534 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.692 |
|
|
\[
{}y^{\prime }-\sin \left (x +y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.217 |
|
|
\[
{}y^{\prime } = 4 y^{2}-3 y+1
\] |
[_quadrature] |
✓ |
1.079 |
|
|
\[
{}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.780 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{x +y}}{x^{2}+2}
\] |
[_separable] |
✓ |
1.739 |
|
|
\[
{}\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x = 0
\] |
[_separable] |
✓ |
1.648 |
|
|
\[
{}s^{2}+s^{\prime } = \frac {s+1}{s t}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
0.920 |
|
|
\[
{}x y^{\prime } = \frac {1}{y^{3}}
\] |
[_separable] |
✓ |
1.955 |
|
|
\[
{}x^{\prime } = 3 x t^{2}
\] |
[_separable] |
✓ |
1.168 |
|
|
\[
{}x^{\prime } = \frac {t \,{\mathrm e}^{-t -2 x}}{x}
\] |
[_separable] |
✓ |
1.386 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2} \sqrt {x +1}}
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}x v^{\prime } = \frac {1-4 v^{2}}{3 v}
\] |
[_separable] |
✓ |
4.040 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (y\right )^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.275 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
100.783 |
|
|
\[
{}x^{\prime }-x^{3} = x
\] |
[_quadrature] |
✓ |
3.894 |
|
|
\[
{}x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.143 |
|
|
\[
{}\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.036 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.584 |
|
|
\[
{}y^{\prime } = x^{3} \left (1-y\right )
\] |
[_separable] |
✓ |
1.402 |
|
|
\[
{}\frac {y^{\prime }}{2} = \sqrt {y+1}\, \cos \left (x \right )
\] |
[_separable] |
✓ |
2.055 |
|
|
\[
{}x^{2} y^{\prime } = \frac {4 x^{2}-x -2}{\left (x +1\right ) \left (y+1\right )}
\] |
[_separable] |
✓ |
3.508 |
|
|
\[
{}\frac {y^{\prime }}{\theta } = \frac {y \sin \left (\theta \right )}{y^{2}+1}
\] |
[_separable] |
✓ |
3.580 |
|
|
\[
{}x^{2}+2 y^{\prime } y = 0
\] |
[_separable] |
✓ |
5.270 |
|
|
\[
{}y^{\prime } = 2 t \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
2.074 |
|
|
\[
{}y^{\prime } = x^{2} \left (y+1\right )
\] |
[_separable] |
✓ |
1.457 |
|
|
\[
{}\sqrt {y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.656 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.522 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x^{2}}}{y^{2}}
\] |
[_separable] |
✓ |
2.783 |
|
|
\[
{}y^{\prime } = \sqrt {\sin \left (x \right )+1}\, \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
21.435 |
|
|
\[
{}y^{\prime } = 2 y-2 t y
\] |
[_separable] |
✓ |
1.695 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.694 |
|
|
\[
{}y^{\prime } = \left (x -3\right ) \left (y+1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
6.533 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
2.168 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.638 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.972 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
4.011 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.675 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (x \right )-y = 0
\] |
[_linear] |
✓ |
1.910 |
|
|
\[
{}x^{\prime }+x t = {\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.940 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime } = t y-y
\] |
[_separable] |
✓ |
1.492 |
|
|
\[
{}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right )
\] |
[_linear] |
✓ |
4.437 |
|
|
\[
{}x x^{\prime }+x t^{2} = \sin \left (t \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.306 |
|
|
\[
{}3 r = r^{\prime }-\theta ^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.289 |
|
|
\[
{}y^{\prime }-y-{\mathrm e}^{3 x} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.029 |
|