|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=4 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.565 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y \\ y^{\prime }=-17 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.548 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.443 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.503 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.576 |
|
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.263 |
|
|
\[
{}x^{\prime } = 3 t^{2}+4 t
\] |
[_quadrature] |
✓ |
0.694 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{t}
\] |
[_quadrature] |
✓ |
0.315 |
|
|
\[
{}x^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.760 |
|
|
\[
{}x^{\prime } = \frac {1}{\sqrt {t^{2}+1}}
\] |
[_quadrature] |
✓ |
0.773 |
|
|
\[
{}x^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.751 |
|
|
\[
{}x^{\prime } = \frac {\cos \left (t \right )}{\sin \left (t \right )}
\] |
[_quadrature] |
✓ |
1.139 |
|
|
\[
{}x^{\prime } = x^{2}-3 x+2
\] |
[_quadrature] |
✓ |
1.634 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.943 |
|
|
\[
{}x^{\prime } = \left (x-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.176 |
|
|
\[
{}x^{\prime } = \sqrt {x^{2}-1}
\] |
[_quadrature] |
✓ |
4.401 |
|
|
\[
{}x^{\prime } = 2 \sqrt {x}
\] |
[_quadrature] |
✓ |
1.583 |
|
|
\[
{}x^{\prime } = \tan \left (x\right )
\] |
[_quadrature] |
✓ |
3.045 |
|
|
\[
{}3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
3.939 |
|
|
\[
{}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
1.881 |
|
|
\[
{}x^{\prime } = \cos \left (\frac {x}{t}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.768 |
|
|
\[
{}\left (t^{2}-x^{2}\right ) x^{\prime } = t x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
18.569 |
|
|
\[
{}{\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t} = 2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.872 |
|
|
\[
{}2 t +3 x+\left (3 t -x\right ) x^{\prime } = t^{2}
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.487 |
|
|
\[
{}x^{\prime }+2 x = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}x^{\prime }+x \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.790 |
|
|
\[
{}x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
1.965 |
|
|
\[
{}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3}
\] |
[_linear] |
✓ |
2.533 |
|
|
\[
{}x^{\prime }+2 t x+t x^{4} = 0
\] |
[_separable] |
✓ |
2.663 |
|
|
\[
{}t x^{\prime }+x \ln \left (t \right ) = t^{2}
\] |
[_linear] |
✓ |
1.352 |
|
|
\[
{}t x^{\prime }+x g \left (t \right ) = h \left (t \right )
\] |
[_linear] |
✓ |
1.165 |
|
|
\[
{}t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.937 |
|
|
\[
{}x^{\prime } = -\lambda x
\] |
[_quadrature] |
✓ |
0.856 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.024 |
|
|
\[
{}x^{\prime \prime }-5 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.842 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.963 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+5 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.105 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.895 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.154 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.052 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.323 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.143 |
|
|
\[
{}x^{\prime \prime }-x = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.182 |
|
|
\[
{}x^{\prime \prime }-x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.219 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
67.877 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }+x = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.315 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.517 |
|
|
\[
{}x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.133 |
|
|
\[
{}y^{\prime }+c y = a
\] |
[_quadrature] |
✓ |
0.872 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+k^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.808 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.395 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x}
\] |
[_separable] |
✓ |
5.431 |
|
|
\[
{}v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.306 |
|
|
\[
{}v^{\prime }+u^{2} v = \sin \left (u \right )
\] |
[_linear] |
✓ |
1.676 |
|
|
\[
{}\sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\] |
[NONE] |
✗ |
0.435 |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3
\] |
[_linear] |
✓ |
2.504 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.977 |
|
|
\[
{}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
26.539 |
|
|
\[
{}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
1.033 |
|
|
\[
{}x^{\prime } = k \left (A -n x\right ) \left (M -m x\right )
\] |
[_quadrature] |
✓ |
7.715 |
|
|
\[
{}y^{\prime } = 1+\frac {1}{x}-\frac {1}{y^{2}+2}-\frac {1}{x \left (y^{2}+2\right )}
\] |
[_separable] |
✓ |
1.595 |
|
|
\[
{}y^{2} = x \left (y-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
39.711 |
|
|
\[
{}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
75.541 |
|
|
\[
{}2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.614 |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right ) y^{\prime }+\sec \left (y\right )^{2} \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
38.659 |
|
|
\[
{}x +y y^{\prime } = m y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.075 |
|
|
\[
{}\frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
34.314 |
|
|
\[
{}\left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime } = \frac {T}{t \sqrt {t^{2}-T^{2}}}-t
\] |
[_exact] |
✓ |
3.225 |
|
|
\[
{}y^{\prime }+x y = x
\] |
[_separable] |
✓ |
1.483 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.446 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {\sin \left (x \right )}{y^{3}}
\] |
[_Bernoulli] |
✓ |
35.661 |
|
|
\[
{}p^{\prime } = \frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )}
\] |
[_linear] |
✓ |
1.175 |
|
|
\[
{}\left (T \ln \left (t \right )-1\right ) T = t T^{\prime }
\] |
[_Bernoulli] |
✓ |
2.440 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
[_linear] |
✓ |
2.412 |
|
|
\[
{}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\] |
[_Bernoulli] |
✓ |
6.082 |
|
|
\[
{}x {y^{\prime }}^{2}-y+2 y^{\prime } = 0
\] |
[_rational, _dAlembert] |
✓ |
0.978 |
|
|
\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
0.347 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{z -y^{\prime }}
\] |
[_quadrature] |
✓ |
0.521 |
|
|
\[
{}\sqrt {t^{2}+T} = T^{\prime }
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.308 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.482 |
|
|
\[
{}\theta ^{\prime \prime } = -p^{2} \theta
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.655 |
|
|
\[
{}\sec \left (\theta \right )^{2} = \frac {m s^{\prime }}{k}
\] |
[_quadrature] |
✓ |
0.350 |
|
|
\[
{}y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.990 |
|
|
\[
{}\phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
58.454 |
|
|
\[
{}y^{\prime } = x \left (a y^{2}+b \right )
\] |
[_separable] |
✓ |
2.460 |
|
|
\[
{}n^{\prime } = \left (n^{2}+1\right ) x
\] |
[_separable] |
✓ |
2.016 |
|
|
\[
{}v^{\prime }+\frac {2 v}{u} = 3 v
\] |
[_separable] |
✓ |
1.684 |
|
|
\[
{}\sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}}
\] |
[_separable] |
✓ |
9.791 |
|
|
\[
{}\sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2}
\] |
[_quadrature] |
✓ |
0.517 |
|
|
\[
{}\frac {y^{\prime }}{x} = y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}}
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = 1+\frac {2 y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.421 |
|
|
\[
{}v^{\prime }+2 v u = 2 u
\] |
[_separable] |
✓ |
1.485 |
|
|
\[
{}1+v^{2}+\left (u^{2}+1\right ) v v^{\prime } = 0
\] |
[_separable] |
✓ |
2.920 |
|
|
\[
{}u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1
\] |
[_separable] |
✓ |
3.790 |
|
|
\[
{}4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
115.909 |
|