|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y}
\] |
[_separable] |
✓ |
1.516 |
|
|
\[
{}y^{\prime }+y^{3} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.523 |
|
|
\[
{}y^{\prime } = \frac {7 x^{2}-1}{7+5 y}
\] |
[_separable] |
✓ |
1.423 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.466 |
|
|
\[
{}y^{\prime } x = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
1.819 |
|
|
\[
{}y y^{\prime } = \left (x +x y^{2}\right ) {\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
2.308 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}}
\] |
[_separable] |
✓ |
1.863 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.168 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1}
\] |
[_separable] |
✓ |
1.907 |
|
|
\[
{}y^{\prime } = 4 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
6.425 |
|
|
\[
{}y^{\prime } = x \left (y-y^{2}\right )
\] |
[_separable] |
✓ |
2.296 |
|
|
\[
{}y^{\prime } = \left (1-12 x \right ) y^{2}
\] |
[_separable] |
✓ |
2.045 |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
4.365 |
|
|
\[
{}x +y \,{\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.654 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{\theta }
\] |
[_separable] |
✓ |
2.052 |
|
|
\[
{}y^{\prime } = \frac {3 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.528 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
3.414 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-3 y}
\] |
[_separable] |
✓ |
2.151 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\] |
[_separable] |
✓ |
3.959 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6}
\] |
[_separable] |
✓ |
6.777 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11}
\] |
[_separable] |
✓ |
3.010 |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
2.012 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
3.415 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}}
\] |
[_separable] |
✓ |
2.677 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
38.212 |
|
|
\[
{}y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
5.147 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y}
\] |
[_separable] |
✓ |
5.960 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6}
\] |
[_separable] |
✓ |
2.343 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
2.056 |
|
|
\[
{}y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.004 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y}
\] |
[_separable] |
✓ |
4.135 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.878 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{3}
\] |
[_separable] |
✓ |
2.748 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{1+t}
\] |
[_separable] |
✓ |
3.295 |
|
|
\[
{}y^{\prime } = \frac {a y+b}{c y+d}
\] |
[_quadrature] |
✓ |
1.347 |
|
|
\[
{}y^{\prime }+4 y = t +{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.682 |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.689 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.651 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.288 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.362 |
|
|
\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.428 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.213 |
|
|
\[
{}2 y^{\prime }+y = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.201 |
|
|
\[
{}t y^{\prime }-y = t^{3} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.384 |
|
|
\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.408 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.306 |
|
|
\[
{}y^{\prime }-y = 2 t \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime }+2 y = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.962 |
|
|
\[
{}t y^{\prime }+4 y = t^{2}-t +1
\] |
[_linear] |
✓ |
1.739 |
|
|
\[
{}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.607 |
|
|
\[
{}y^{\prime }-2 y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.459 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.689 |
|
|
\[
{}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.553 |
|
|
\[
{}t y^{\prime }+\left (1+t \right ) y = t
\] |
[_linear] |
✓ |
1.479 |
|
|
\[
{}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.525 |
|
|
\[
{}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.447 |
|
|
\[
{}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.594 |
|
|
\[
{}t y^{\prime }+\left (1+t \right ) y = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.961 |
|
|
\[
{}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.511 |
|
|
\[
{}\sin \left (t \right ) y^{\prime }+\cos \left (t \right ) y = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
38.480 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.677 |
|
|
\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.043 |
|
|
\[
{}y^{\prime }-y = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.576 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.725 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.521 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.361 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.258 |
|
|
\[
{}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t
\] |
[_linear] |
✓ |
2.865 |
|
|
\[
{}t \left (t -4\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.972 |
|
|
\[
{}y^{\prime }+\tan \left (t \right ) y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.921 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
2.173 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
1.940 |
|
|
\[
{}\ln \left (t \right ) y^{\prime }+y = \cot \left (t \right )
\] |
[_linear] |
✓ |
2.792 |
|
|
\[
{}y^{\prime } = \frac {t -y}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.734 |
|
|
\[
{}y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.368 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.116 |
|
|
\[
{}y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.375 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.362 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1}
\] |
[_separable] |
✓ |
1.606 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.948 |
|
|
\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.415 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
6.197 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
2.282 |
|
|
\[
{}y^{\prime }+y^{3} = 0
\] |
[_quadrature] |
✓ |
1.904 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )}
\] |
[_separable] |
✓ |
2.177 |
|
|
\[
{}y^{\prime } = t y \left (3-y\right )
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.602 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.579 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.694 |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
1.258 |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.109 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.082 |
|
|
\[
{}3 x^{2}-2 x y+2+\left (6 y^{2}-x^{2}+3\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.361 |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.122 |
|
|
\[
{}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.664 |
|
|
\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.419 |
|