|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y+1}{1+t}
\] |
[_separable] |
✓ |
1.823 |
|
|
\[
{}y^{\prime } = \frac {y+2}{2 t +1}
\] |
[_separable] |
✓ |
1.907 |
|
|
\[
{}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.914 |
|
|
\[
{}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.946 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right )
\] |
[_separable] |
✓ |
3.151 |
|
|
\[
{}y^{\prime }+k y = 0
\] |
[_quadrature] |
✓ |
0.670 |
|
|
\[
{}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0
\] |
[_separable] |
✓ |
40.459 |
|
|
\[
{}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.776 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 y+10 t}
\] |
[_separable] |
✓ |
2.440 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
2.523 |
|
|
\[
{}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.490 |
|
|
\[
{}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\] |
[_separable] |
✓ |
36.320 |
|
|
\[
{}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}
\] |
[_separable] |
✓ |
36.437 |
|
|
\[
{}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0
\] |
[_separable] |
✓ |
2.150 |
|
|
\[
{}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.427 |
|
|
\[
{}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0
\] |
[_separable] |
✓ |
39.865 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}
\] |
[_separable] |
✓ |
1.806 |
|
|
\[
{}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}
\] |
[_separable] |
✓ |
5.931 |
|
|
\[
{}\frac {x -2}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\] |
[_separable] |
✓ |
2.114 |
|
|
\[
{}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
42.965 |
|
|
\[
{}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )}
\] |
[_separable] |
✓ |
42.356 |
|
|
\[
{}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}
\] |
[_separable] |
✓ |
1.338 |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
2.144 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
2.366 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.501 |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0
\] |
[_separable] |
✓ |
2.314 |
|
|
\[
{}y^{\prime } = \sin \left (t -y\right )+\sin \left (y+t \right )
\] |
[_separable] |
✓ |
4.787 |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
2.364 |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
2.776 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
4.053 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
3.652 |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
3.390 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
4.059 |
|
|
\[
{}y^{\prime } = x^{3}
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}y^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.699 |
|
|
\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
4.000 |
|
|
\[
{}\sin \left (y \right )^{2} = x^{\prime }
\] |
[_quadrature] |
✓ |
0.821 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
5.729 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.923 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
2.371 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t -y}
\] |
[_separable] |
✓ |
3.057 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
4.425 |
|
|
\[
{}y^{\prime } = t \sin \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.844 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.689 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1}
\] |
[_separable] |
✓ |
2.868 |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
2.491 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.835 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
3.970 |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
2.373 |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
2.200 |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
2.123 |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.311 |
|
|
\[
{}y^{\prime } = -\frac {y-2}{x -2}
\] |
[_separable] |
✓ |
2.309 |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.766 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.770 |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.446 |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
1.938 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.317 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
1.322 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.694 |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
2.133 |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
1.713 |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
1.187 |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
1.135 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.325 |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.250 |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.266 |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
1.519 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
2.368 |
|
|
\[
{}y^{\prime } x +y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.174 |
|
|
\[
{}y^{\prime } x +y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
1.139 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.678 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
1.894 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
2.751 |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.779 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
1.892 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
3.243 |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
3.177 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.787 |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
1.688 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.401 |
|
|
\[
{}y^{\prime } = \frac {1}{x +y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.057 |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.189 |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.043 |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
1.795 |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
1.585 |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.159 |
|
|
\[
{}y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.453 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.351 |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
1.993 |
|
|
\[
{}y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.781 |
|
|
\[
{}t y^{\prime }+y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.540 |
|
|
\[
{}t y^{\prime }+y = 2 t \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.467 |
|
|
\[
{}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
1.809 |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.808 |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.488 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 t}+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.443 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.142 |
|