|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (1+x^{2}+y^{2}\right ) y^{\prime }+2 x y+x^{2}+3 = 0
\] |
[_exact, _rational] |
✓ |
1.310 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.932 |
|
|
\[
{}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.994 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }+x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
1.048 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }-4 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.281 |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.138 |
|
|
\[
{}2 x y y^{\prime }+3 x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
61.533 |
|
|
\[
{}\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.782 |
|
|
\[
{}\left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.047 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.693 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.609 |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.756 |
|
|
\[
{}\left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2} = 0
\] |
[_rational] |
✓ |
1.636 |
|
|
\[
{}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0
\] |
[_separable] |
✓ |
2.062 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
1.683 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.954 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.255 |
|
|
\[
{}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.116 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.298 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{2} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.078 |
|
|
\[
{}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.802 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.050 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.222 |
|
|
\[
{}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.670 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.147 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.974 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.472 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.062 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.093 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
6.228 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.571 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.875 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.955 |
|
|
\[
{}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.235 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.149 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.623 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.646 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.154 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
29.989 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.492 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.985 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}+2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.110 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.058 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.559 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.278 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.496 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.431 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.015 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.302 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.115 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.134 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.943 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.732 |
|
|
\[
{}y^{\prime \prime }+9 y = 8 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.580 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.715 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.606 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.053 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.354 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.269 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.027 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.164 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.418 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.472 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.111 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.708 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.472 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.590 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.505 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.779 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.823 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.264 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.428 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.402 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.816 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.632 |
|
|
\[
{}y^{3} y^{\prime \prime } = k
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.084 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}-1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.160 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.944 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.175 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.532 |
|