|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (1+y\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.595 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.789 |
|
|
\[
{}2 y^{\prime } = 3 \left (y-2\right )^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.750 |
|
|
\[
{}\left (x +x y\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
2.184 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.265 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = 1
\] |
[_linear] |
✓ |
0.245 |
|
|
\[
{}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0
\] |
[_linear] |
✓ |
0.272 |
|
|
\[
{}2 y^{\prime } x +y = 2 x^{{5}/{2}}
\] |
[_linear] |
✓ |
0.224 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
0.403 |
|
|
\[
{}y^{\prime }+\frac {y}{\sqrt {x^{2}+1}} = \frac {1}{x +\sqrt {x^{2}+1}}
\] |
[_linear] |
✓ |
0.286 |
|
|
\[
{}\left (1+{\mathrm e}^{x}\right ) y^{\prime }+2 y \,{\mathrm e}^{x} = \left (1+{\mathrm e}^{x}\right ) {\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.297 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y = \ln \left (x \right )
\] |
[_linear] |
✓ |
0.131 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y+2 x \sqrt {-x^{2}+1}
\] |
[_linear] |
✓ |
0.259 |
|
|
\[
{}y^{\prime }+y \tanh \left (x \right ) = 2 \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
0.321 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
0.332 |
|
|
\[
{}x^{\prime } = \cos \left (y \right )-x \tan \left (y \right )
\] |
[_linear] |
✓ |
0.300 |
|
|
\[
{}x^{\prime }+x-{\mathrm e}^{y} = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.258 |
|
|
\[
{}x^{\prime } = \frac {3 y^{{2}/{3}}-x}{3 y}
\] |
[_linear] |
✓ |
0.215 |
|
|
\[
{}y^{\prime }+y = x y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
1.280 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = 2 x^{{3}/{2}} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
8.544 |
|
|
\[
{}3 x y^{2} y^{\prime }+3 y^{3} = 1
\] |
[_separable] |
✓ |
2.981 |
|
|
\[
{}2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.753 |
|
|
\[
{}\left (x -y\right ) y^{\prime }+y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.541 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
unknown |
✓ |
42.423 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.396 |
|
|
\[
{}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.375 |
|
|
\[
{}x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.539 |
|
|
\[
{}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.440 |
|
|
\[
{}y^{\prime } = \cos \left (x +y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.552 |
|
|
\[
{}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.140 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0
\] |
[_linear] |
✓ |
2.747 |
|
|
\[
{}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.904 |
|
|
\[
{}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.793 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.456 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.108 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.217 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.030 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.536 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.292 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.346 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.105 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.998 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.115 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.123 |
|
|
\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.716 |
|
|
\[
{}y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.727 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.137 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 16
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.311 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime \prime }+y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.144 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 12 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.449 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.362 |
|
|
\[
{}y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.390 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.320 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.015 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.672 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.584 |
|
|
\[
{}5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
49.080 |
|
|
\[
{}y^{\prime \prime }+9 y = 30 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.004 |
|
|
\[
{}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.159 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.625 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.395 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
50.924 |
|
|
\[
{}5 y^{\prime \prime }+6 y^{\prime }+2 y = x^{2}+6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
40.347 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime } = 2 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.239 |
|
|
\[
{}y^{\prime \prime }+y = 2 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.150 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 12 x \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.439 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.469 |
|
|
\[
{}y^{\prime \prime }+y = 8 x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.667 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}-1+2 \cos \left (x \right )+\left (2-4 x \right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.652 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.437 |
|
|
\[
{}y^{\prime \prime }-y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.845 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right )+4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.510 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.620 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.819 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.843 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.739 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.687 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.202 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.864 |
|
|
\[
{}2 y y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.348 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.718 |
|
|
\[
{}{y^{\prime \prime }}^{2} = k^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.763 |
|
|
\[
{}k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear]] |
✓ |
3.757 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.159 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.041 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.154 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.690 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -16 y = 8 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.945 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = x -\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.314 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.879 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 6 x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.855 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.526 |
|