|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 \sqrt {x y}-y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.934 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.199 |
|
|
\[
{}2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.537 |
|
|
\[
{}y-1-x y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.042 |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.805 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.355 |
|
|
\[
{}y y^{\prime \prime }-y y^{\prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.454 |
|
|
\[
{}2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.787 |
|
|
\[
{}y^{\prime } = \frac {1}{x y+x^{3} y^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.631 |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (y-1+x \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
1.720 |
|
|
\[
{}{\mathrm e}^{x}+3 y^{2}+2 x y y^{\prime } = 0
\] |
[_Bernoulli] |
✓ |
1.562 |
|
|
\[
{}x y+2 x^{3} y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.326 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.524 |
|
|
\[
{}y^{\prime \prime \prime } = 2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.253 |
|
|
\[
{}y+3 y^{2} x^{4}+\left (x +2 x^{2} y^{3}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.516 |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
67.682 |
|
|
\[
{}2 y \left (x \,{\mathrm e}^{x^{2}}+y \sin \left (x \right ) \cos \left (x \right )\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime } = 0
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
12.457 |
|
|
\[
{}\cos \left (y\right )+\sin \left (y\right ) \left (x -\sin \left (y\right ) \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.775 |
|
|
\[
{}y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.902 |
|
|
\[
{}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
6.964 |
|
|
\[
{}2 x^{3} y y^{\prime }+3 y^{2} x^{2}+7 = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.951 |
|
|
\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.346 |
|
|
\[
{}x^{2} \left (-y+x y^{\prime }\right ) = y \left (x +y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.816 |
|
|
\[
{}y^{4}+x y+\left (x y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.628 |
|
|
\[
{}x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.394 |
|
|
\[
{}x y^{\prime \prime } = x +y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.185 |
|
|
\[
{}y+\left (x y-x -y^{3}\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.787 |
|
|
\[
{}y+2 y^{3} y^{\prime } = \left (x +4 y \ln \left (y\right )\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.294 |
|
|
\[
{}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.398 |
|
|
\[
{}2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.344 |
|
|
\[
{}2 x +y \cos \left (x y\right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
5.745 |
|
|
\[
{}y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.414 |
|
|
\[
{}2 y^{\prime }+x = 4 \sqrt {y}
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
2.749 |
|
|
\[
{}2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x = y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.663 |
|
|
\[
{}y^{\prime }-6 x \,{\mathrm e}^{x -y}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.228 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.081 |
|
|
\[
{}y \sin \left (x \right )+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
2.187 |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.327 |
|
|
\[
{}y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right ) = 1
\] |
[_quadrature] |
✓ |
0.788 |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) = 0
\] |
[_linear] |
✓ |
3.345 |
|
|
\[
{}x +\sin \left (\frac {y}{x}\right )^{2} \left (y-x y^{\prime }\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.577 |
|
|
\[
{}2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-y^{2} x^{2}-3 x \right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✓ |
4.389 |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.615 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\left (6\right )}-64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.417 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.539 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.096 |
|
|
\[
{}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.240 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
16.444 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )+x \cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.581 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
1.080 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+x \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.201 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime }+y = 9 \,{\mathrm e}^{2 x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.164 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 48 x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime } = 9 x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.113 |
|
|
\[
{}y^{\left (5\right )}+4 y^{\prime \prime \prime } = 7+x
\] |
[[_high_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 64 \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y = 44 \sin \left (3 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y = 5 \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+5 y = 5 \,{\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 4 \,{\mathrm e}^{-x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.464 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.690 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime } = 2 \,{\mathrm e}^{x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.118 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x} \left (x +1\right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 4 \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.000 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.624 |
|
|
\[
{}y^{\prime \prime }-y = 12 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.363 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )-3 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.881 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \left (x^{2}+10\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }-4 y = 96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.416 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (x \right )+10 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.184 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.156 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x \,{\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.809 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 15 \sin \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.154 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 \sin \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 10 \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.147 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime }-4 y = 50 \sin \left (x \right )+50 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.196 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 32 \,{\mathrm e}^{2 x}+16 x^{3}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y = 72 \,{\mathrm e}^{3 x}+729 x^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{x}-\frac {2}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }-y = \frac {1}{\sinh \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.582 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.103 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.477 |
|