|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.969 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x = x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.903 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.110 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.225 |
|
|
\[
{}y^{\prime }+2 y = 2
\] |
[_quadrature] |
✓ |
0.216 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.261 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.348 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.463 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.425 |
|
|
\[
{}y^{\prime \prime \prime }-y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.385 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.278 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.251 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.279 |
|
|
\[
{}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.366 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.774 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.097 |
|
|
\[
{}y^{\prime \prime }+y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.442 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.538 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.540 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.520 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.479 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }-y x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.433 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
1.603 |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.587 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.602 |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (y^{2}+3 x^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
80.528 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.748 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.796 |
|
|
\[
{}y^{\prime \prime }-y = 4-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{x} \left (1-x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.981 |
|
|
\[
{}4 y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
1.454 |
|
|
\[
{}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.295 |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}1+y-\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.267 |
|
|
\[
{}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.410 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.452 |
|
|
\[
{}y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
1.637 |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
4.516 |
|
|
\[
{}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.246 |
|
|
\[
{}1+2 y-\left (4-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.373 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
1.182 |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.976 |
|
|
\[
{}2 y^{\prime } x -2 y = \sqrt {x^{2}+4 y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.108 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.290 |
|
|
\[
{}x y y^{\prime } = \left (1+y\right ) \left (1-x \right )
\] |
[_separable] |
✓ |
1.162 |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.253 |
|
|
\[
{}y \left (2 y x +1\right )+x \left (1-y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.558 |
|
|
\[
{}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.849 |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
8.584 |
|
|
\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.282 |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
1.908 |
|
|
\[
{}x^{2}+y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.404 |
|
|
\[
{}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.470 |
|
|
\[
{}y^{2}+y x -y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.475 |
|
|
\[
{}y^{\prime } = -2 \left (2 x +3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
9.362 |
|
|
\[
{}x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.294 |
|
|
\[
{}x^{2}-y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.156 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
0.305 |
|
|
\[
{}x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.178 |
|
|
\[
{}2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.305 |
|
|
\[
{}4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.434 |
|
|
\[
{}2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
0.243 |
|
|
\[
{}x \sqrt {x^{2}+y^{2}}-y+\left (y \sqrt {x^{2}+y^{2}}-x \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.301 |
|
|
\[
{}x +y+1-\left (y-x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.290 |
|
|
\[
{}y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 y \left (x +1\right )\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
0.329 |
|
|
\[
{}2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.301 |
|
|
\[
{}y \left (x -2 y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.842 |
|
|
\[
{}x^{2}+y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.356 |
|
|
\[
{}x^{2}+y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.637 |
|
|
\[
{}1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.418 |
|
|
\[
{}x +y+1-\left (x -y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.701 |
|
|
\[
{}x -x^{2}-y^{2}+y y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
0.354 |
|
|
\[
{}2 y-3 x +y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.175 |
|
|
\[
{}x -y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.309 |
|
|
\[
{}-y-3 x^{2} \left (x^{2}+y^{2}\right )+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
0.359 |
|
|
\[
{}y-\ln \left (x \right )-y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.186 |
|
|
\[
{}3 x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.295 |
|
|
\[
{}y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.480 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.355 |
|
|
\[
{}2 y-3 x y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.704 |
|
|
\[
{}y+x \left (x^{2} y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.282 |
|
|
\[
{}y+x^{3} y+2 x^{2}+\left (x +4 x y^{4}+8 y^{3}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
0.296 |
|
|
\[
{}-y-x^{2} {\mathrm e}^{x}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.209 |
|
|
\[
{}1+y^{2} = \left (x^{2}+x \right ) y^{\prime }
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}2 y-x^{3}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.184 |
|
|
\[
{}y+\left (-x +y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.389 |
|
|
\[
{}3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.494 |
|
|
\[
{}3 x^{2} y^{2}+4 \left (x^{3} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.223 |
|
|
\[
{}y \left (x +y\right )-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
0.229 |
|
|
\[
{}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.412 |
|
|
\[
{}y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.678 |
|