|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}-y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
0.162 |
|
|
\[
{}y^{\prime }+y = 2+2 x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.993 |
|
|
\[
{}y^{\prime }-y = y x
\] |
[_separable] |
✓ |
1.135 |
|
|
\[
{}-3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
2.395 |
|
|
\[
{}i^{\prime }-6 i = 10 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime }+y = y^{2} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.081 |
|
|
\[
{}y+\left (y x +x -3 y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.020 |
|
|
\[
{}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right )
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.570 |
|
|
\[
{}y^{\prime } x +y-x^{3} y^{6} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.119 |
|
|
\[
{}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0
\] |
[_linear] |
✓ |
1.576 |
|
|
\[
{}y \left (1+y^{2}\right ) = 2 \left (1-2 x y^{2}\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.543 |
|
|
\[
{}y y^{\prime }-x y^{2}+x = 0
\] |
[_separable] |
✓ |
1.590 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.607 |
|
|
\[
{}2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right ) = 0
\] |
[_Bernoulli] |
✓ |
7.676 |
|
|
\[
{}y^{\prime } x = y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
26.710 |
|
|
\[
{}2+y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.147 |
|
|
\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.622 |
|
|
\[
{}2 x y^{5}-y+2 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.587 |
|
|
\[
{}1+\sin \left (y\right ) = \left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
70.222 |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.506 |
|
|
\[
{}L i^{\prime }+R i = E \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.575 |
|
|
\[
{}x^{2} \cos \left (y\right ) y^{\prime } = 2 x \sin \left (y\right )-1
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.339 |
|
|
\[
{}4 x^{2} y y^{\prime } = 3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3}
\] |
[_rational] |
✗ |
1.264 |
|
|
\[
{}x y^{3}-y^{3}-x^{2} {\mathrm e}^{x}+3 x y^{2} y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
2.240 |
|
|
\[
{}y^{\prime }+x \left (x +y\right ) = x^{3} \left (x +y\right )^{3}-1
\] |
[_Abel] |
✓ |
1.769 |
|
|
\[
{}y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.799 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
2.801 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-x \left (-1+y\right ) = 0
\] |
[_quadrature] |
✓ |
1.626 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.493 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.139 |
|
|
\[
{}8 y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.684 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.734 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.303 |
|
|
\[
{}16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.577 |
|
|
\[
{}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.702 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.190 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
202.584 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.426 |
|
|
\[
{}y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.469 |
|
|
\[
{}y = 2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
2.796 |
|
|
\[
{}y {y^{\prime }}^{2}-y^{\prime } x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.398 |
|
|
\[
{}y = y^{\prime } x -2 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.296 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.705 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.455 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.628 |
|
|
\[
{}\left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y
\] |
[_quadrature] |
✓ |
0.400 |
|
|
\[
{}y = -y^{\prime } x +x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.997 |
|
|
\[
{}2 y = {y^{\prime }}^{2}+4 y^{\prime } x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.341 |
|
|
\[
{}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
146.084 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y y^{\prime }\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.345 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.765 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.022 |
|
|
\[
{}y^{\prime \prime }+9 y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.496 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.040 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+y^{\prime } x -y = 3 x^{4}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.238 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.233 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.350 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 2
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.237 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.504 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.757 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.755 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.652 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.801 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.917 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.099 |
|
|
\[
{}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5
\] |
[[_high_order, _missing_x]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.952 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.046 |
|
|
\[
{}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.809 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.070 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.159 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.876 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.137 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.569 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.371 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.256 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime \prime }+2 y = 2+{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.165 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.635 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.995 |
|
|
\[
{}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.782 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.037 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.173 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
37.485 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }+y = \cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.132 |
|