|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y^{2}-3 y+2
\] |
[_quadrature] |
✓ |
1.317 |
|
|
\[
{}4 \left (x -1\right )^{2} y^{\prime }-3 \left (y+3\right )^{2} = 0
\] |
[_separable] |
✓ |
2.063 |
|
|
\[
{}y^{\prime } = \sin \left (t -y\right )+\sin \left (y+t \right )
\] |
[_separable] |
✓ |
5.320 |
|
|
\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
2.212 |
|
|
\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
2.634 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
3.928 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
3.510 |
|
|
\[
{}y^{\prime } = y^{3}-y
\] |
[_quadrature] |
✓ |
3.219 |
|
|
\[
{}y^{\prime } = y^{3}+y
\] |
[_quadrature] |
✓ |
3.982 |
|
|
\[
{}y^{\prime } = x^{3}
\] |
[_quadrature] |
✓ |
0.447 |
|
|
\[
{}y^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}1 = \cos \left (y\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
4.036 |
|
|
\[
{}\sin \left (y \right )^{2} = x^{\prime }
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {t}}{y}
\] |
[_separable] |
✓ |
6.410 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y}{t}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
15.338 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1}
\] |
[_separable] |
✓ |
2.233 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t -y}
\] |
[_separable] |
✓ |
2.854 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (y\right )}
\] |
[_quadrature] |
✓ |
4.572 |
|
|
\[
{}y^{\prime } = t \sin \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.706 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.521 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1}
\] |
[_separable] |
✓ |
2.927 |
|
|
\[
{}y^{\prime } = \frac {y+3}{3 x +1}
\] |
[_separable] |
✓ |
2.151 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.485 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
3.696 |
|
|
\[
{}y^{\prime } = \frac {3 y+1}{x +3}
\] |
[_separable] |
✓ |
2.069 |
|
|
\[
{}y^{\prime } = y \cos \left (t \right )
\] |
[_separable] |
✓ |
1.841 |
|
|
\[
{}y^{\prime } = y^{2} \cos \left (t \right )
\] |
[_separable] |
✓ |
1.898 |
|
|
\[
{}y^{\prime } = \sqrt {y}\, \cos \left (t \right )
\] |
[_separable] |
✓ |
2.073 |
|
|
\[
{}y^{\prime }+y f \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.462 |
|
|
\[
{}y^{\prime } = -\frac {y-2}{-2+x}
\] |
[_separable] |
✓ |
1.955 |
|
|
\[
{}y^{\prime } = \frac {x +y+3}{3 x +3 y+1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime } = \frac {x -y+2}{2 x -2 y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}y^{\prime } = \left (x +y-4\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.735 |
|
|
\[
{}y^{\prime } = \left (3 y+1\right )^{4}
\] |
[_quadrature] |
✓ |
1.794 |
|
|
\[
{}y^{\prime } = 3 y
\] |
[_quadrature] |
✓ |
1.051 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
1.011 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.398 |
|
|
\[
{}y^{\prime } = 16 y-8 y^{2}
\] |
[_quadrature] |
✓ |
1.852 |
|
|
\[
{}y^{\prime } = 12+4 y-y^{2}
\] |
[_quadrature] |
✓ |
1.568 |
|
|
\[
{}y^{\prime } = y f \left (t \right )
\] |
[_separable] |
✓ |
1.262 |
|
|
\[
{}y^{\prime }-y = 10
\] |
[_quadrature] |
✓ |
0.929 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.111 |
|
|
\[
{}y^{\prime }-y = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.240 |
|
|
\[
{}y^{\prime }-y = t^{2}-2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime }-y = 4 t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.152 |
|
|
\[
{}t y^{\prime }+y = t^{2}
\] |
[_linear] |
✓ |
1.266 |
|
|
\[
{}t y^{\prime }+y = t
\] |
[_linear] |
✓ |
1.875 |
|
|
\[
{}x y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.079 |
|
|
\[
{}x y^{\prime }+y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.480 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
1.779 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
2.753 |
|
|
\[
{}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.722 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
1.741 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
3.270 |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
3.119 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.772 |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
1.579 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.119 |
|
|
\[
{}y^{\prime } = \frac {1}{x +y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
0.977 |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.972 |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.990 |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
1.368 |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
1.216 |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime }-y = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.132 |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
2.170 |
|
|
\[
{}y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.464 |
|
|
\[
{}t y^{\prime }+y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.457 |
|
|
\[
{}t y^{\prime }+y = 2 t \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.327 |
|
|
\[
{}\left ({\mathrm e}^{t}+1\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
1.737 |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.589 |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.291 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 t}+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.289 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\] |
[[_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‘]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime }-y = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.294 |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.109 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.947 |
|
|
\[
{}y^{\prime }+y = 2-{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.086 |
|
|
\[
{}y^{\prime }-5 y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.010 |
|
|
\[
{}y^{\prime }+3 y = 27 t^{2}+9
\] |
[[_linear, ‘class A‘]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.821 |
|
|
\[
{}y^{\prime }+4 y = 8 \cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.424 |
|
|
\[
{}y^{\prime }+10 y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.114 |
|
|
\[
{}y^{\prime }-3 y = 27 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.059 |
|
|
\[
{}y^{\prime }-y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }+y = 4+3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.186 |
|
|
\[
{}y^{\prime }+y = 2 \cos \left (t \right )+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.483 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime }-\frac {y}{2} = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.452 |
|
|
\[
{}t y^{\prime }+y = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.219 |
|
|
\[
{}y^{\prime }+y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.256 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.519 |
|
|
\[
{}y^{\prime }+y = \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.483 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.314 |
|
|
\[
{}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
57.323 |
|