|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
5.401 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.859 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.977 |
|
|
\[
{}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.853 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.899 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.269 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.251 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.608 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.643 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.628 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.013 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x^{2}+2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.293 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.763 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.992 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.084 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.182 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.721 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.801 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.717 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.714 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.525 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }+9 y = 8 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.903 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.269 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.145 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.285 |
|
|
\[
{}y^{\prime \prime }+y = \cot \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.131 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.995 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.776 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.768 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.969 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.641 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.059 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.075 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.143 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.014 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.140 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.040 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.747 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.606 |
|
|
\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.090 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.251 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.131 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y = \frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.659 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.571 |
|
|
\[
{}y^{3} y^{\prime \prime } = k
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.103 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2}-1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.079 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.859 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.030 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.423 |
|
|
\[
{}r^{\prime \prime } = -\frac {k}{r^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
70.945 |
|
|
\[
{}y^{\prime \prime } = \frac {3 k y^{2}}{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.976 |
|
|
\[
{}y^{\prime \prime } = 2 k y^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.803 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.542 |
|
|
\[
{}r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.184 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.589 |
|
|
\[
{}y y^{\prime \prime }-3 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.325 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.681 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.312 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.588 |
|
|
\[
{}y^{\prime \prime } = y^{\prime } {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime } = 2 y y^{\prime }
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.921 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
17.669 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.142 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.299 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.192 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.706 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.087 |
|
|
\[
{}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
9.163 |
|
|
\[
{}a x y^{3}+b y^{2}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
2.039 |
|
|
\[
{}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\] |
[_Abel] |
✓ |
3.962 |
|
|
\[
{}y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0
\] |
[_Abel] |
✗ |
4.625 |
|
|
\[
{}x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.573 |
|
|
\[
{}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.290 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.203 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.052 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.961 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{a x}+a y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.647 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right )^{3} = a^{2} {y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.617 |
|
|
\[
{}\left (x +1\right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.197 |
|
|
\[
{}y^{\prime } = a y^{2} x
\] |
[_separable] |
✓ |
1.368 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.632 |
|
|
\[
{}x y \left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.800 |
|
|
\[
{}\frac {x}{1+y} = \frac {y y^{\prime }}{x +1}
\] |
[_separable] |
✓ |
1.474 |
|
|
\[
{}y^{\prime }+b^{2} y^{2} = a^{2}
\] |
[_quadrature] |
✓ |
0.802 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.629 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right ) = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.956 |
|
|
\[
{}a x y^{\prime }+2 y = x y y^{\prime }
\] |
[_separable] |
✓ |
1.381 |
|
|
\[
{}x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.959 |
|