|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.557 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t -y}
\] |
[_separable] |
✓ |
2.241 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime } = t \sin \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.479 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.472 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1}
\] |
[_separable] |
✓ |
3.279 |
|
|
\[
{}y^{\prime } = \frac {3+y}{3 x +1}
\] |
[_separable] |
✓ |
1.706 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.140 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
2.658 |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
1.717 |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
1.584 |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
1.781 |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
1.781 |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = -\frac {y-2}{x -2}
\] |
[_separable] |
✓ |
1.580 |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.118 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.119 |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.879 |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
0.796 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
0.494 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
0.591 |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
0.837 |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
0.616 |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
1.170 |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.902 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.864 |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.034 |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
1.122 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
1.636 |
|
|
\[
{}y^{\prime } x +y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.966 |
|
|
\[
{}y^{\prime } x +y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
0.935 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.296 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
1.570 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
2.471 |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.471 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
1.503 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
2.990 |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
2.951 |
|
|
\[
{}y^{\prime }+2 \cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.577 |
|
|
\[
{}y^{\prime }+y x = x^{3}
\] |
[_linear] |
✓ |
1.336 |
|
|
\[
{}y^{\prime }-y x = x
\] |
[_separable] |
✓ |
0.992 |
|
|
\[
{}y^{\prime } = \frac {1}{x +y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.811 |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.730 |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
1.243 |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
1.060 |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.823 |
|
|
\[
{}y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.042 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.967 |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
1.972 |
|
|
\[
{}y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.258 |
|
|
\[
{}t y^{\prime }+y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.302 |
|
|
\[
{}t y^{\prime }+y = 2 t \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.132 |
|
|
\[
{}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
1.540 |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.335 |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 t}+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.071 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
0.865 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.508 |
|
|
\[
{}y^{\prime }-y = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.128 |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.957 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.815 |
|
|
\[
{}y^{\prime }+y = 2-{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.931 |
|
|
\[
{}y^{\prime }-5 y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.845 |
|
|
\[
{}y^{\prime }+3 y = 27 t^{2}+9
\] |
[[_linear, ‘class A‘]] |
✓ |
0.885 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.660 |
|
|
\[
{}y^{\prime }+4 y = 8 \cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime }+10 y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.988 |
|
|
\[
{}y^{\prime }-3 y = 27 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.885 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.830 |
|
|
\[
{}y^{\prime }+y = 4+3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.980 |
|
|
\[
{}y^{\prime }+y = 2 \cos \left (t \right )+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.254 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.296 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.296 |
|
|
\[
{}t y^{\prime }+y = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.102 |
|
|
\[
{}y^{\prime }+y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.017 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.329 |
|
|
\[
{}y^{\prime }+y = \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.092 |
|
|
\[
{}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
85.125 |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
2.674 |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.401 |
|
|
\[
{}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
19.092 |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.739 |
|
|
\[
{}t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.600 |
|
|
\[
{}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.873 |
|
|
\[
{}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
1.498 |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
1.634 |
|
|
\[
{}3 t^{2}-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.248 |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.641 |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.500 |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.591 |
|
|
\[
{}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.247 |
|
|
\[
{}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.662 |
|