|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime }-x = \delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.319 |
|
|
\[
{}x^{\prime \prime }+x = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.332 |
|
|
\[
{}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.167 |
|
|
\[
{}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.489 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.620 |
|
|
\[
{}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.933 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.528 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.512 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.357 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.443 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.378 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 y \\ y^{\prime }=6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.389 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=-x-14 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.112 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y-3 x \\ y^{\prime }=x+2 y-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.917 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.727 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.536 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.364 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.390 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.432 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.380 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.432 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y+1 \\ y^{\prime }=x+y+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.669 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\cos \left (w t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.662 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+3 \\ y^{\prime }=7 x+5 y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.864 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}y^{\prime }+y = x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.465 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.321 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.050 |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.311 |
|
|
\[
{}y^{\prime } x +y = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.821 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.444 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.071 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.704 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.640 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.987 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.000 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.842 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.879 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.151 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.198 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (y\right )
\] |
[_separable] |
✓ |
3.421 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x -2}
\] |
[_separable] |
✓ |
2.478 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.996 |
|
|
\[
{}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.966 |
|
|
\[
{}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.420 |
|
|
\[
{}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.207 |
|
|
\[
{}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.149 |
|
|
\[
{}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.551 |
|
|
\[
{}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.138 |
|
|
\[
{}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.287 |
|
|
\[
{}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\] |
[_separable] |
✓ |
3.434 |
|
|
\[
{}\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.633 |
|
|
\[
{}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.622 |
|
|
\[
{}3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
5.303 |
|
|
\[
{}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
76.670 |
|
|
\[
{}y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.099 |
|
|
\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.220 |
|
|
\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
4.495 |
|
|
\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.337 |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.881 |
|
|
\[
{}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.882 |
|
|
\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.766 |
|
|
\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.669 |
|
|
\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.434 |
|
|
\[
{}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.340 |
|
|
\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
[_separable] |
✓ |
2.633 |
|
|
\[
{}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0
\] |
[_separable] |
✓ |
2.692 |
|
|
\[
{}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.402 |
|
|
\[
{}x +y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.501 |
|
|
\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.259 |
|
|
\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.179 |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.615 |
|