|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
3.603 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
3.781 |
|
|
\[
{}y^{\prime } = y^{2}-4
\] |
[_quadrature] |
✓ |
6.924 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.259 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
3.322 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.660 |
|
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.653 |
|
|
\[
{}2 x \sin \left (y\right )^{2}-\left (x^{2}+10\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.332 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.383 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}+\frac {1}{100}
\] |
[_quadrature] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}-\frac {1}{100}
\] |
[_quadrature] |
✓ |
2.346 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
11.508 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
10.030 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
10.071 |
|
|
\[
{}y^{\prime } = y-y^{3}
\] |
[_quadrature] |
✓ |
12.147 |
|
|
\[
{}y^{\prime } = \frac {1}{y-3}
\] |
[_quadrature] |
✓ |
2.167 |
|
|
\[
{}y^{\prime } = \frac {1}{y-3}
\] |
[_quadrature] |
✓ |
2.086 |
|
|
\[
{}y^{\prime } = \frac {1}{y-3}
\] |
[_quadrature] |
✓ |
2.012 |
|
|
\[
{}y^{\prime } = \frac {1}{y-3}
\] |
[_quadrature] |
✓ |
2.059 |
|
|
\[
{}y^{\prime } = \frac {1}{\sin \left (x \right )+1}
\] |
[_quadrature] |
✓ |
0.693 |
|
|
\[
{}y^{\prime } = \frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}}
\] |
[_separable] |
✓ |
21.139 |
|
|
\[
{}\left (\sqrt {x}+x \right ) y^{\prime } = \sqrt {y}+y
\] |
[_separable] |
✓ |
9.463 |
|
|
\[
{}y^{\prime } = y^{{2}/{3}}-y
\] |
[_quadrature] |
✓ |
114.622 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{\sqrt {x}}}{y}
\] |
[_separable] |
✓ |
4.902 |
|
|
\[
{}y^{\prime } = \frac {x \arctan \left (x \right )}{y}
\] |
[_separable] |
✓ |
5.394 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
3.669 |
|
|
\[
{}y^{\prime } = x \sqrt {y}
\] |
[_separable] |
✓ |
4.344 |
|
|
\[
{}y^{\prime } = \sqrt {1+y^{2}}\, \sin \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
4.483 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
2.758 |
|
|
\[
{}y^{\prime } = y+\frac {y}{\ln \left (x \right ) x}
\] |
[_separable] |
✓ |
2.806 |
|
|
\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.736 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {1-y^{2}}{-x^{2}+1}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.486 |
|
|
\[
{}m^{\prime } = -\frac {k}{m^{2}}
\] |
[_quadrature] |
✓ |
4.767 |
|
|
\[
{}u^{\prime } = a \sqrt {1+u^{2}}
\] |
[_quadrature] |
✓ |
3.500 |
|
|
\[
{}x^{\prime } = k \left (A -x\right )^{2}
\] |
[_quadrature] |
✓ |
4.258 |
|
|
\[
{}1+{x^{\prime }}^{2} = \frac {a}{y}
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\] |
[_separable] |
✓ |
5.638 |
|
|
\[
{}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\] |
[_separable] |
✓ |
5.466 |
|
|
\[
{}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\] |
[_separable] |
✓ |
4.516 |
|
|
\[
{}y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\] |
[_separable] |
✓ |
4.427 |
|
|
\[
{}\left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x = 0
\] |
[_separable] |
✓ |
2.214 |
|
|
\[
{}y^{\prime } = \frac {x \left (1-x \right )}{y \left (y-2\right )}
\] |
[_separable] |
✓ |
7.845 |
|
|
\[
{}y^{\prime } = \frac {x \left (1-x \right )}{y \left (y-2\right )}
\] |
[_separable] |
✓ |
6.795 |
|
|
\[
{}y^{\prime } = 5 y
\] |
[_quadrature] |
✓ |
1.637 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
1.720 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.347 |
|
|
\[
{}3 y^{\prime }+12 y = 4
\] |
[_quadrature] |
✓ |
1.679 |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
1.550 |
|
|
\[
{}y^{\prime }+2 x y = x^{3}
\] |
[_linear] |
✓ |
1.597 |
|
|
\[
{}x^{2} y^{\prime }+x y = 1
\] |
[_linear] |
✓ |
1.283 |
|
|
\[
{}y^{\prime } = 2 y+x^{2}+5
\] |
[[_linear, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}-y+x y^{\prime } = x^{2} \sin \left (x \right )
\] |
[_linear] |
✓ |
1.605 |
|
|
\[
{}x y^{\prime }+2 y = 3
\] |
[_separable] |
✓ |
2.452 |
|
|
\[
{}x y^{\prime }+4 y = x^{3}-x
\] |
[_linear] |
✓ |
1.478 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x y = x^{2}+x
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.513 |
|
|
\[
{}x y^{\prime }+\left (x +1\right ) y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.441 |
|
|
\[
{}y-4 \left (x +y^{6}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.850 |
|
|
\[
{}y = \left (y \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.325 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1
\] |
[_linear] |
✓ |
2.045 |
|
|
\[
{}\cos \left (x \right )^{2} \sin \left (x \right ) y^{\prime }+\cos \left (x \right )^{3} y = 1
\] |
[_linear] |
✓ |
5.395 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (x +2\right ) y = 2 x \,{\mathrm e}^{-x}
\] |
[_linear] |
✓ |
1.903 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime } = 5-8 y-4 x y
\] |
[_linear] |
✓ |
1.836 |
|
|
\[
{}r^{\prime }+r \sec \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
2.135 |
|
|
\[
{}p^{\prime }+2 t p = p+4 t -2
\] |
[_separable] |
✓ |
1.618 |
|
|
\[
{}x y^{\prime }+\left (3 x +1\right ) y = {\mathrm e}^{-3 x}
\] |
[_linear] |
✓ |
2.031 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
1.456 |
|
|
\[
{}y^{\prime } = x +5 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime } = 2 x -3 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.557 |
|
|
\[
{}x y^{\prime }+y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.456 |
|
|
\[
{}y y^{\prime }-x = 2 y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
3.668 |
|
|
\[
{}L i^{\prime }+R i = E
\] |
[_quadrature] |
✓ |
1.417 |
|
|
\[
{}T^{\prime } = k \left (T-T_{m} \right )
\] |
[_quadrature] |
✓ |
1.065 |
|
|
\[
{}x y^{\prime }+y = 4 x +1
\] |
[_linear] |
✓ |
2.084 |
|
|
\[
{}y^{\prime }+4 x y = x^{3} {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.771 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \ln \left (x \right )
\] |
[_linear] |
✓ |
1.556 |
|
|
\[
{}x \left (x +1\right ) y^{\prime }+x y = 1
\] |
[_linear] |
✓ |
1.530 |
|
|
\[
{}y^{\prime }-y \sin \left (x \right ) = 2 \sin \left (x \right )
\] |
[_separable] |
✓ |
2.415 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) y = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.207 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.933 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.888 |
|
|
\[
{}y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[_linear] |
✓ |
0.977 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right .
\] |
[_linear] |
✓ |
0.849 |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x
\] |
[_linear] |
✓ |
1.733 |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
2.315 |
|
|
\[
{}y^{\prime }-2 x y = 1
\] |
[_linear] |
✓ |
1.455 |
|
|
\[
{}y^{\prime }-2 x y = -1
\] |
[_linear] |
✓ |
1.441 |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 1
\] |
[_linear] |
✓ |
1.725 |
|
|
\[
{}x^{2} y^{\prime }-y = x^{3}
\] |
[_linear] |
✓ |
1.506 |
|
|
\[
{}x^{3} y^{\prime }+2 x^{2} y = 10 \sin \left (x \right )
\] |
[_linear] |
✓ |
1.791 |
|
|
\[
{}y^{\prime }-\sin \left (x^{2}\right ) y = 0
\] |
[_separable] |
✓ |
5.128 |
|
|
\[
{}1 = \left (x +y^{2}\right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.166 |
|
|
\[
{}y+\left (2 x +x y-3\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.211 |
|
|
\[
{}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.769 |
|
|
\[
{}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\] |
[_linear] |
✗ |
1.607 |
|
|
\[
{}x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.474 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\lambda _{1} x \\ y^{\prime }=\lambda _{1} x-\lambda _{2} y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.369 |
|
|
\[
{}e^{\prime } = -\frac {e}{r c}
\] |
[_quadrature] |
✓ |
1.390 |
|
|
\[
{}2 x -1+\left (3 y+7\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.094 |
|