|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x-2 y=0 \\ 2 x+y^{\prime }-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.608 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-3 x+2 y=0 \\ y^{\prime }-x+3 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.573 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x-z=0 \\ x+y^{\prime }-y=0 \\ z^{\prime }+x+2 y-3 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2}+2 y-3 z \\ y^{\prime }=y-\frac {z}{2} \\ z^{\prime }=-2 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.858 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=y \\ x^{\prime }-y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=t \\ x^{\prime }-y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }=x+y-t \\ 2 x^{\prime }+3 y^{\prime }=2 x+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }-y^{\prime }=t \\ 3 x^{\prime }+2 y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} 5 x^{\prime }-3 y^{\prime }=x+y \\ 3 x^{\prime }-y^{\prime }=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 y^{\prime }=0 \\ 2 x^{\prime }-3 y^{\prime }=y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.348 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }=\sin \left (t \right ) \\ x^{\prime }-2 y^{\prime }=x+y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }=-5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.672 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }=-12 x+5 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.720 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }=-10 x+9 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.965 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }=-6 x+16 y+6 \cosh \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.186 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }=-x+3 y+z+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.007 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\ y^{\prime }=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\ z^{\prime }=-x+6 y+z+9 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.891 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y+4 z \\ y^{\prime }=-2 x+y+2 z \\ z^{\prime }=-4 x-2 y+6 z+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.609 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+3 z \\ y^{\prime }=x-y+2 z+2 \,{\mathrm e}^{-t} \\ z^{\prime }=-2 x+2 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.811 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.613 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }=9 x-3 y+12 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.876 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }=3 x+14 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }=-5 x+2 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.620 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y+z \\ y^{\prime }=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }=5 x+y+z+39 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
25.722 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }=y+z-10 \cos \left (t \right ) \\ z^{\prime }=x+z+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.494 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.381 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\ y^{\prime }=4 x-y+2 z+4 \,{\mathrm e}^{t} \\ z^{\prime }=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.448 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y+10 \sinh \left (t \right ) \\ y^{\prime }=19 x-13 y+24 \sinh \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.304 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x-3 y-6 t \\ y^{\prime }=-x+11 y+10 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.330 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.376 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{{3}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.432 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.417 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.737 |
|
|
\[
{}y^{\prime \prime }+y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.832 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.046 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.813 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0
\] |
[_Jacobi] |
✓ |
0.723 |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.641 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.703 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.973 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.113 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.162 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.816 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.169 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.935 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.691 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.712 |
|
|
\[
{}y^{\prime \prime }-\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.079 |
|
|
\[
{}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.974 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.912 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.736 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.194 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.420 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.914 |
|
|
\[
{}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }
\] |
[_rational] |
✓ |
116.954 |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.184 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.835 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.005 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.662 |
|
|
\[
{}y-y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.602 |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
[_separable] |
✓ |
1.427 |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.881 |
|
|
\[
{}\left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
[_separable] |
✓ |
1.664 |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.879 |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
[_separable] |
✓ |
1.434 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.052 |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
[_separable] |
✓ |
2.087 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.746 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
1.976 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
4.473 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.983 |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.046 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.615 |
|
|
\[
{}x +y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
2.349 |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.545 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.309 |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.013 |
|
|
\[
{}2 \sqrt {s t}-s+t s^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.275 |
|
|
\[
{}t -s+t s^{\prime } = 0
\] |
[_linear] |
✓ |
1.500 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.851 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) \left (y+y^{\prime } x \right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.896 |
|
|
\[
{}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.993 |
|
|
\[
{}x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.837 |
|
|
\[
{}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.403 |
|
|
\[
{}\frac {y-y^{\prime } x}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.733 |
|
|
\[
{}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
68.203 |
|
|
\[
{}y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.194 |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.498 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3}
\] |
[_linear] |
✓ |
1.546 |
|
|
\[
{}y^{\prime }-\frac {a y}{x} = \frac {x +1}{x}
\] |
[_linear] |
✓ |
1.247 |
|
|
\[
{}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.343 |
|
|
\[
{}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\] |
[_linear] |
✓ |
1.947 |
|
|
\[
{}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\] |
[_linear] |
✓ |
2.166 |
|
|
\[
{}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\] |
[_linear] |
✓ |
1.170 |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
0.935 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.169 |
|
|
\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\] |
[_linear] |
✓ |
1.623 |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
1.228 |
|