|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.713 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.410 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 4 t
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.422 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
2.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
19.786 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
12.804 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.621 |
|
|
\[
{}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.267 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.539 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.632 |
|
|
\[
{}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.549 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.049 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.881 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-7 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.655 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}3 y^{\prime \prime }+5 y^{\prime }-2 y = 3 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.391 |
|
|
\[
{}y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.128 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}-\frac {3 y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.619 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+2 y=0 \\ y^{\prime }+y-x=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x-2 y=0 \\ 2 x+y^{\prime }-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.596 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-3 x+2 y=0 \\ y^{\prime }-x+3 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x-z=0 \\ x+y^{\prime }-y=0 \\ z^{\prime }+x+2 y-3 z=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2}+2 y-3 z \\ y^{\prime }=y-\frac {z}{2} \\ z^{\prime }=-2 x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.975 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=y \\ x^{\prime }-y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=t \\ x^{\prime }-y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }=x+y-t \\ 2 x^{\prime }+3 y^{\prime }=2 x+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.488 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }-y^{\prime }=t \\ 3 x^{\prime }+2 y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.438 |
|
|
\[
{}\left [\begin {array}{c} 5 x^{\prime }-3 y^{\prime }=x+y \\ 3 x^{\prime }-y^{\prime }=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 y^{\prime }=0 \\ 2 x^{\prime }-3 y^{\prime }=y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.395 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }=\sin \left (t \right ) \\ x^{\prime }-2 y^{\prime }=x+y+t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.730 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }=-5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.753 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }=-12 x+5 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.872 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }=-10 x+9 y+37 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.178 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }=-6 x+16 y+6 \cosh \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.399 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }=-x+3 y+z+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.429 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\ y^{\prime }=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\ z^{\prime }=-x+6 y+z+9 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.008 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y+4 z \\ y^{\prime }=-2 x+y+2 z \\ z^{\prime }=-4 x-2 y+6 z+{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.718 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+3 z \\ y^{\prime }=x-y+2 z+2 \,{\mathrm e}^{-t} \\ z^{\prime }=-2 x+2 y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.834 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.672 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }=9 x-3 y+12 \cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.107 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }=3 x+14 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.701 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }=-5 x+2 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.706 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y+z \\ y^{\prime }=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }=5 x+y+z+39 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
30.730 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }=y+z-10 \cos \left (t \right ) \\ z^{\prime }=x+z+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.825 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.825 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\ y^{\prime }=4 x-y+2 z+4 \,{\mathrm e}^{t} \\ z^{\prime }=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.773 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y+10 \sinh \left (t \right ) \\ y^{\prime }=19 x-13 y+24 \sinh \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.666 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x-3 y-6 t \\ y^{\prime }=-x+11 y+10 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.108 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{{3}/{2}} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \sec \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.485 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.042 |
|
|
\[
{}y^{\prime \prime }+y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.726 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.891 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.683 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-5 x \right ) y^{\prime }-4 y = 0
\] |
[_Jacobi] |
✓ |
0.549 |
|
|
\[
{}\left (x^{2}-1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.456 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.586 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }-k y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.101 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.136 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.694 |
|
|
\[
{}x \left (-1+x \right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.293 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.804 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.597 |
|
|
\[
{}x y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.443 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }-\alpha ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.617 |
|
|
\[
{}y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.155 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.933 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.288 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.456 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime }-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.422 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.904 |
|
|
\[
{}x y \left (1-{y^{\prime }}^{2}\right ) = \left (x^{2}-y^{2}-a^{2}\right ) y^{\prime }
\] |
[_rational] |
✓ |
123.821 |
|
|
\[
{}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.686 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.845 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.466 |
|
|
\[
{}y-x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.660 |
|
|
\[
{}\left (1+u \right ) v+\left (1-v\right ) u v^{\prime } = 0
\] |
[_separable] |
✓ |
1.484 |
|
|
\[
{}1+y-\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.052 |
|
|
\[
{}\left (t^{2}+x t^{2}\right ) x^{\prime }+x^{2}+t x^{2} = 0
\] |
[_separable] |
✓ |
1.737 |
|
|
\[
{}y-a +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
0.888 |
|
|
\[
{}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0
\] |
[_separable] |
✓ |
1.445 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.284 |
|
|
\[
{}1+s^{2}-\sqrt {t}\, s^{\prime } = 0
\] |
[_separable] |
✓ |
1.980 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.792 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
22.960 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-\sqrt {1-y^{2}} = 0
\] |
[_separable] |
✓ |
25.861 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.485 |
|
|
\[
{}x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.719 |
|
|
\[
{}y-x +\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.345 |
|
|
\[
{}x +y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
2.813 |
|
|
\[
{}x +y+\left (y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.467 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.257 |
|
|
\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.297 |
|