|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = {\mathrm e}^{3 y+2 t}
\] |
[_separable] |
✓ |
2.331 |
|
|
\[
{}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.564 |
|
|
\[
{}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }
\] |
[_separable] |
✓ |
36.513 |
|
|
\[
{}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}
\] |
[_separable] |
✓ |
30.786 |
|
|
\[
{}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0
\] |
[_separable] |
✓ |
2.236 |
|
|
\[
{}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.470 |
|
|
\[
{}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0
\] |
[_separable] |
✓ |
39.885 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )}
\] |
[_separable] |
✓ |
1.895 |
|
|
\[
{}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}}
\] |
[_separable] |
✓ |
5.839 |
|
|
\[
{}\frac {x -2}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}}
\] |
[_separable] |
✓ |
2.167 |
|
|
\[
{}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right )
\] |
[_separable] |
✓ |
43.704 |
|
|
\[
{}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )}
\] |
[_separable] |
✓ |
40.509 |
|
|
\[
{}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}
\] |
[_separable] |
✓ |
1.359 |
|
|
\[
{}y^{\prime } = \frac {5^{-t}}{y^{2}}
\] |
[_separable] |
✓ |
2.322 |
|
|
\[
{}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1
\] |
[_separable] |
✓ |
2.384 |
|
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.356 |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0
\] |
[_separable] |
✓ |
2.256 |
|
|
\[
{}y^{\prime } = \sin \left (t -y\right )+\sin \left (y+t \right )
\] |
[_separable] |
✓ |
4.634 |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
2.408 |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
2.724 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
3.651 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
3.676 |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
2.413 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
3.684 |
|
|
\[
{}y^{\prime } = x^{3}
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}y^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.753 |
|
|
\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
4.239 |
|
|
\[
{}\sin \left (y \right )^{2} = x^{\prime }
\] |
[_quadrature] |
✓ |
0.806 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
9.605 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.591 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
2.799 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t -y}
\] |
[_separable] |
✓ |
3.141 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
4.668 |
|
|
\[
{}y^{\prime } = t \sin \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.868 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.792 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1}
\] |
[_separable] |
✓ |
3.066 |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
2.561 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
3.091 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
4.121 |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
2.472 |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
2.293 |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
2.260 |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
2.415 |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.335 |
|
|
\[
{}y^{\prime } = -\frac {y-2}{x -2}
\] |
[_separable] |
✓ |
2.474 |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.878 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.905 |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.748 |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
1.990 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.391 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
1.320 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.591 |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
1.887 |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
1.484 |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
1.069 |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
1.181 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.406 |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.262 |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime } t +y = t^{2}
\] |
[_linear] |
✓ |
1.557 |
|
|
\[
{}y^{\prime } t +y = t
\] |
[_linear] |
✓ |
2.537 |
|
|
\[
{}y+y^{\prime } x = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.237 |
|
|
\[
{}y+y^{\prime } x = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
1.253 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.776 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
1.986 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
2.975 |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.934 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
1.988 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
3.439 |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
3.410 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.007 |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
1.569 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.480 |
|
|
\[
{}y^{\prime } = \frac {1}{y^{2}+x}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.245 |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.215 |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.154 |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
1.856 |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
1.641 |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.229 |
|
|
\[
{}y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
2.151 |
|
|
\[
{}y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.826 |
|
|
\[
{}y^{\prime } t +y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.629 |
|
|
\[
{}y^{\prime } t +y = 2 t \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.497 |
|
|
\[
{}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
1.929 |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.911 |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.550 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 t}+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.515 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
1.210 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.805 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.734 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.706 |
|
|
\[
{}y^{\prime }-y = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.497 |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.326 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime }+y = 2-{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.318 |
|
|
\[
{}y^{\prime }-5 y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.252 |
|
|
\[
{}y^{\prime }+3 y = 27 t^{2}+9
\] |
[[_linear, ‘class A‘]] |
✓ |
1.303 |
|