|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t y^{\prime }+y = t^{3}
\] |
[_linear] |
✓ |
2.048 |
|
|
\[
{}t^{3} y^{\prime }+t^{4} y = 2 t^{3}
\] |
[_linear] |
✓ |
1.414 |
|
|
\[
{}2 y^{\prime }+t y = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.834 |
|
|
\[
{}y^{\prime }+y \sec \left (t \right ) = t
\] |
[_linear] |
✓ |
2.660 |
|
|
\[
{}y^{\prime }+\frac {y}{t -3} = \frac {1}{t -1}
\] |
[_linear] |
✓ |
1.928 |
|
|
\[
{}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2}
\] |
[_linear] |
✓ |
1.920 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.191 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t
\] |
[_linear] |
✓ |
2.958 |
|
|
\[
{}t y^{\prime }+y = t \sin \left (t \right )
\] |
[_linear] |
✓ |
1.790 |
|
|
\[
{}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.565 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
2.408 |
|
|
\[
{}y^{\prime } = t y^{2}
\] |
[_separable] |
✓ |
2.415 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
12.175 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
3.831 |
|
|
\[
{}y^{\prime } = \frac {x}{y^{2}}
\] |
[_separable] |
✓ |
2.576 |
|
|
\[
{}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.491 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x^{2}}
\] |
[_separable] |
✓ |
4.229 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{y}
\] |
[_quadrature] |
✓ |
2.240 |
|
|
\[
{}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.185 |
|
|
\[
{}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.367 |
|
|
\[
{}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right )
\] |
[_separable] |
✓ |
3.957 |
|
|
\[
{}y^{\prime } = \frac {y+1}{t +1}
\] |
[_separable] |
✓ |
1.970 |
|
|
\[
{}y^{\prime } = \frac {y+2}{2 t +1}
\] |
[_separable] |
✓ |
2.072 |
|
|
\[
{}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.085 |
|
|
\[
{}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.254 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right )
\] |
[_separable] |
✓ |
3.939 |
|
|
\[
{}y^{\prime }+k y = 0
\] |
[_quadrature] |
✓ |
0.916 |
|
|
\[
{}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0
\] |
[_separable] |
✓ |
42.954 |
|
|
\[
{}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
11.536 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 y+10 t}
\] |
[_separable] |
✓ |
2.828 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
2.983 |
|
|
\[
{}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.688 |
|
|
\[
{}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\] |
[_separable] |
✓ |
36.946 |
|
|
\[
{}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}
\] |
[_separable] |
✓ |
37.648 |
|
|
\[
{}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0
\] |
[_separable] |
✓ |
2.580 |
|
|
\[
{}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.973 |
|
|
\[
{}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0
\] |
[_separable] |
✓ |
42.296 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}
\] |
[_separable] |
✓ |
2.283 |
|
|
\[
{}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}
\] |
[_separable] |
✓ |
7.577 |
|
|
\[
{}\frac {-2+x}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\] |
[_separable] |
✓ |
2.287 |
|
|
\[
{}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
42.127 |
|
|
\[
{}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )}
\] |
[_separable] |
✓ |
44.849 |
|
|
\[
{}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}
\] |
[_separable] |
✓ |
1.678 |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
3.006 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
2.350 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.844 |
|
|
\[
{}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0
\] |
[_separable] |
✓ |
3.040 |
|
|
\[
{}y^{\prime } = \sin \left (-y+t \right )+\sin \left (y+t \right )
\] |
[_separable] |
✓ |
4.020 |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
48.253 |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
35.710 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
5.299 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
19.919 |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
4.778 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
5.289 |
|
|
\[
{}y^{\prime } = x^{3}
\] |
[_quadrature] |
✓ |
0.663 |
|
|
\[
{}y^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.774 |
|
|
\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
18.374 |
|
|
\[
{}\sin \left (y \right )^{2} = x^{\prime }
\] |
[_quadrature] |
✓ |
0.935 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
26.976 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
23.066 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
2.845 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-y+t}
\] |
[_separable] |
✓ |
3.898 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
2.915 |
|
|
\[
{}y^{\prime } = t \sin \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.860 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1}
\] |
[_separable] |
✓ |
3.619 |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
2.588 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
3.375 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
5.449 |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
2.432 |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
3.491 |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
2.494 |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
3.010 |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
0.862 |
|
|
\[
{}y^{\prime } = -\frac {y-2}{-2+x}
\] |
[_separable] |
✓ |
2.352 |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.913 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.913 |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.338 |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
2.427 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.684 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
1.669 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
2.055 |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
2.512 |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
2.185 |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
0.872 |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
1.378 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.605 |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.468 |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
1.527 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
2.956 |
|
|
\[
{}x y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.306 |
|
|
\[
{}x y^{\prime }+y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
1.286 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.820 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
2.156 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
3.386 |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
2.027 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
2.192 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
3.817 |
|