|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.637 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.443 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}x^{\prime }+3 x = {\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.458 |
|
|
\[
{}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
0.391 |
|
|
\[
{}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.487 |
|
|
\[
{}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.453 |
|
|
\[
{}x^{\prime }+x = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.522 |
|
|
\[
{}x^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.161 |
|
|
\[
{}x^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.175 |
|
|
\[
{}x^{\prime \prime } = \cos \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.317 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.168 |
|
|
\[
{}x^{\prime \prime }+x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.195 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.197 |
|
|
\[
{}x^{\prime \prime }+x = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.183 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime } = 12 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.195 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.178 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.305 |
|
|
\[
{}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.243 |
|
|
\[
{}x^{\prime \prime }+x = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.404 |
|
|
\[
{}y^{\prime } = \frac {x^{4}}{y}
\] |
[_separable] |
✓ |
2.264 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (x^{3}+1\right )}{y}
\] |
[_separable] |
✓ |
1.888 |
|
|
\[
{}y^{\prime }+y^{3} \sin \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.886 |
|
|
\[
{}y^{\prime } = \frac {7 x^{2}-1}{7+5 y}
\] |
[_separable] |
✓ |
1.848 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )^{2} \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.885 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.884 |
|
|
\[
{}y y^{\prime } = \left (x +x y^{2}\right ) {\mathrm e}^{x^{2}}
\] |
[_separable] |
✓ |
2.678 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}}
\] |
[_separable] |
✓ |
2.113 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{1+y^{2}}
\] |
[_separable] |
✓ |
1.266 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right )^{2}}{y^{3}+1}
\] |
[_separable] |
✓ |
2.145 |
|
|
\[
{}y^{\prime } = 4 \sqrt {x y}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
10.180 |
|
|
\[
{}y^{\prime } = x \left (y-y^{2}\right )
\] |
[_separable] |
✓ |
2.395 |
|
|
\[
{}y^{\prime } = \left (1-12 x \right ) y^{2}
\] |
[_separable] |
✓ |
2.338 |
|
|
\[
{}y^{\prime } = \frac {3-2 x}{y}
\] |
[_separable] |
✓ |
4.025 |
|
|
\[
{}x +y \,{\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.650 |
|
|
\[
{}r^{\prime } = \frac {r^{2}}{\theta }
\] |
[_separable] |
✓ |
2.196 |
|
|
\[
{}y^{\prime } = \frac {3 x}{y+x^{2} y}
\] |
[_separable] |
✓ |
2.936 |
|
|
\[
{}y^{\prime } = \frac {2 x}{2 y+1}
\] |
[_separable] |
✓ |
3.646 |
|
|
\[
{}y^{\prime } = 2 x y^{2}+4 x^{3} y^{2}
\] |
[_separable] |
✓ |
2.445 |
|
|
\[
{}y^{\prime } = x^{2} {\mathrm e}^{-3 y}
\] |
[_separable] |
✓ |
2.379 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (2 x \right )
\] |
[_separable] |
✓ |
4.298 |
|
|
\[
{}y^{\prime } = \frac {x \left (x^{2}+1\right ) y^{5}}{6}
\] |
[_separable] |
✓ |
11.221 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11}
\] |
[_separable] |
✓ |
3.544 |
|
|
\[
{}x^{2} y^{\prime } = y-x y
\] |
[_separable] |
✓ |
2.105 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y}
\] |
[_separable] |
✓ |
4.902 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-4}}
\] |
[_separable] |
✓ |
3.234 |
|
|
\[
{}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
37.115 |
|
|
\[
{}y^{2} \sqrt {-x^{2}+1}\, y^{\prime } = \arcsin \left (x \right )
\] |
[_separable] |
✓ |
3.542 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+1}{12 y^{2}-12 y}
\] |
[_separable] |
✓ |
8.195 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}}{2 y^{2}-6}
\] |
[_separable] |
✓ |
3.015 |
|
|
\[
{}y^{\prime } = 2 y^{2}+x y^{2}
\] |
[_separable] |
✓ |
2.449 |
|
|
\[
{}y^{\prime } = \frac {6-{\mathrm e}^{x}}{3+2 y}
\] |
[_separable] |
✓ |
3.671 |
|
|
\[
{}y^{\prime } = \frac {2 \cos \left (2 x \right )}{10+2 y}
\] |
[_separable] |
✓ |
5.786 |
|
|
\[
{}y^{\prime } = 2 \left (x +1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.904 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{3}
\] |
[_separable] |
✓ |
3.178 |
|
|
\[
{}y^{\prime } = \frac {t y \left (4-y\right )}{t +1}
\] |
[_separable] |
✓ |
3.894 |
|
|
\[
{}y^{\prime } = \frac {a y+b}{c y+d}
\] |
[_quadrature] |
✓ |
2.078 |
|
|
\[
{}y^{\prime }+4 y = t +{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.512 |
|
|
\[
{}y^{\prime }-2 y = t^{2} {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.934 |
|
|
\[
{}y^{\prime }+y = t \,{\mathrm e}^{-t}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.977 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 5+\cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.916 |
|
|
\[
{}y^{\prime }-2 y = 3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.387 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.594 |
|
|
\[
{}y^{\prime }+2 t y = 16 t \,{\mathrm e}^{-t^{2}}
\] |
[_linear] |
✓ |
2.793 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime }+4 t y = \frac {1}{\left (t^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
2.455 |
|
|
\[
{}2 y^{\prime }+y = 3 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.323 |
|
|
\[
{}t y^{\prime }-y = t^{3} {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.533 |
|
|
\[
{}y^{\prime }+y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.582 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime }-y = 2 t \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.637 |
|
|
\[
{}y^{\prime }+2 y = t \,{\mathrm e}^{-2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.219 |
|
|
\[
{}t y^{\prime }+4 y = t^{2}-t +1
\] |
[_linear] |
✓ |
1.891 |
|
|
\[
{}y^{\prime }+\frac {2 y}{t} = \frac {\cos \left (t \right )}{t^{2}}
\] |
[_linear] |
✓ |
1.713 |
|
|
\[
{}y^{\prime }-2 y = {\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.666 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.837 |
|
|
\[
{}t^{3} y^{\prime }+4 t^{2} y = {\mathrm e}^{-t}
\] |
[_linear] |
✓ |
1.673 |
|
|
\[
{}t y^{\prime }+\left (t +1\right ) y = t
\] |
[_linear] |
✓ |
1.536 |
|
|
\[
{}y^{\prime }-\frac {y}{3} = 3 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.726 |
|
|
\[
{}2 y^{\prime }-y = {\mathrm e}^{\frac {t}{3}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.511 |
|
|
\[
{}3 y^{\prime }-2 y = {\mathrm e}^{-\frac {\pi t}{2}}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.754 |
|
|
\[
{}t y^{\prime }+\left (t +1\right ) y = 2 t \,{\mathrm e}^{-t}
\] |
[_linear] |
✓ |
2.171 |
|
|
\[
{}t y^{\prime }+2 y = \frac {\sin \left (t \right )}{t}
\] |
[_linear] |
✓ |
1.727 |
|
|
\[
{}\sin \left (t \right ) y^{\prime }+\cos \left (t \right ) y = {\mathrm e}^{t}
\] |
[_linear] |
✓ |
36.165 |
|
|
\[
{}y^{\prime }+\frac {y}{2} = 2 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.860 |
|
|
\[
{}y^{\prime }+\frac {4 y}{3} = 1-\frac {t}{4}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.443 |
|
|
\[
{}y^{\prime }+\frac {y}{4} = 3+2 \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.197 |
|
|
\[
{}y^{\prime }-y = 1+3 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.779 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2} = 3 t +3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.705 |
|
|
\[
{}y^{\prime }-6 y = t^{6} {\mathrm e}^{6 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.888 |
|
|
\[
{}y^{\prime }+\frac {y}{t} = 3 \cos \left (2 t \right )
\] |
[_linear] |
✓ |
1.625 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.580 |
|
|
\[
{}2 y^{\prime }+y = 3 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.315 |
|
|
\[
{}\left (t -3\right ) y^{\prime }+\ln \left (t \right ) y = 2 t
\] |
[_linear] |
✓ |
2.954 |
|
|
\[
{}t \left (-4+t \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.909 |
|
|
\[
{}y^{\prime }+\tan \left (t \right ) y = \sin \left (t \right )
\] |
[_linear] |
✓ |
2.043 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
2.313 |
|
|
\[
{}\left (-t^{2}+4\right ) y^{\prime }+2 t y = 3 t^{2}
\] |
[_linear] |
✓ |
2.098 |
|
|
\[
{}\ln \left (t \right ) y^{\prime }+y = \cot \left (t \right )
\] |
[_linear] |
✓ |
2.690 |
|
|
\[
{}y^{\prime } = \frac {-y+t}{2 t +5 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.680 |
|
|
\[
{}y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.528 |
|