|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.383 |
|
|
\[
{}\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.795 |
|
|
\[
{}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.204 |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
2.880 |
|
|
\[
{}x +y^{\prime } y = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
1.749 |
|
|
\[
{}y = 2 y^{\prime } x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.776 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.488 |
|
|
\[
{}y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.354 |
|
|
\[
{}y = y {y^{\prime }}^{2}+2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.862 |
|
|
\[
{}y = y^{\prime } y+y^{\prime }-{y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.348 |
|
|
\[
{}y = y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.458 |
|
|
\[
{}y = y^{\prime } x +y^{\prime }
\] |
[_separable] |
✓ |
1.782 |
|
|
\[
{}y = y^{\prime } x +\frac {1}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.370 |
|
|
\[
{}y = y^{\prime } x -\frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.628 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\] |
[_linear] |
✓ |
2.544 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.074 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
2.531 |
|
|
\[
{}x y^{\prime \prime \prime } = 2
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime } = a^{2} y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.135 |
|
|
\[
{}y^{\prime \prime } = \frac {a}{y^{3}}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.161 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.376 |
|
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.703 |
|
|
\[
{}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.840 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
2.516 |
|
|
\[
{}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2}
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime \prime } = 9 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.441 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.196 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.296 |
|
|
\[
{}y^{\prime \prime }+12 y = 7 y^{\prime }
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.107 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.915 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.431 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.215 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.345 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.362 |
|
|
\[
{}s^{\prime \prime }-a^{2} s = 1+t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.712 |
|
|
\[
{}y^{\prime \prime }-y = 5 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.391 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.033 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 2-6 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.196 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.543 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.061 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.063 |
|
|
\[
{}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.579 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.497 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.640 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.985 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.346 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+1 \\ y^{\prime }=x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.668 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.598 |
|
|
\[
{}y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.898 |
|
|
\[
{}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\] |
[_separable] |
✓ |
2.858 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.046 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\] |
[_linear] |
✓ |
1.848 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.950 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.984 |
|
|
\[
{}y^{\prime } x +y-y^{2} \ln \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
1.839 |
|
|
\[
{}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.711 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.022 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.723 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}y^{\prime } = y^{2}+x
\] |
[[_Riccati, _special]] |
✓ |
1.803 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.594 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.611 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.588 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.687 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.380 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.395 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.387 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}x^{\prime \prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.221 |
|
|
\[
{}x^{\prime \prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.662 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.756 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.737 |
|
|
\[
{}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.555 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|