|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime \prime }-x^{\prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.119 |
|
|
\[
{}x^{\prime \prime \prime }-8 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.371 |
|
|
\[
{}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.609 |
|
|
\[
{}x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.520 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }-6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.318 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.325 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}x^{\prime \prime }-x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.174 |
|
|
\[
{}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.338 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.384 |
|
|
\[
{}x^{\prime \prime }-2 x = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.331 |
|
|
\[
{}x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.561 |
|
|
\[
{}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.842 |
|
|
\[
{}x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.613 |
|
|
\[
{}x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.774 |
|
|
\[
{}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.935 |
|
|
\[
{}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.882 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.791 |
|
|
\[
{}x^{\prime \prime }-x = \delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.532 |
|
|
\[
{}x^{\prime \prime }+x = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.545 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.674 |
|
|
\[
{}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.643 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.006 |
|
|
\[
{}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.169 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.524 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.482 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.445 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.615 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 y \\ y^{\prime }=6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=-x-14 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.237 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y-3 x \\ y^{\prime }=x+2 y-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.969 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.591 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.707 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.574 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.351 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.305 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.542 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y+1 \\ y^{\prime }=x+y+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.667 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.509 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\cos \left (w t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.778 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+3 \\ y^{\prime }=7 x+5 y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.914 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.436 |
|
|
\[
{}y^{\prime }+y = x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.514 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.148 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.870 |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
58.829 |
|
|
\[
{}x y^{\prime }+y = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.405 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.882 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.505 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.845 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.437 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.371 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.069 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.169 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.417 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.638 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.634 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.464 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.179 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (y\right )
\] |
[_separable] |
✓ |
3.608 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{-2+x}
\] |
[_separable] |
✓ |
2.594 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.236 |
|
|
\[
{}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.781 |
|
|
\[
{}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.563 |
|
|
\[
{}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.307 |
|
|
\[
{}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.213 |
|
|
\[
{}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.757 |
|
|
\[
{}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.647 |
|
|
\[
{}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.036 |
|
|
\[
{}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\] |
[_separable] |
✓ |
3.924 |
|