|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.240 |
|
|
\[
{}{y^{\prime }}^{2}-a \,x^{3} = 0
\] |
[_quadrature] |
✓ |
0.233 |
|
|
\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (y+2 x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
5.684 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{4}
\] |
[_quadrature] |
✓ |
0.319 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
4.984 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
1.401 |
|
|
\[
{}x -y y^{\prime } = a {y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
80.742 |
|
|
\[
{}y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\] |
[_quadrature] |
✓ |
61.075 |
|
|
\[
{}4 y = x^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.510 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.437 |
|
|
\[
{}y = 2 y^{\prime }+3 {y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.686 |
|
|
\[
{}x \left ({y^{\prime }}^{2}+1\right ) = 1
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}x^{2} = a^{2} \left ({y^{\prime }}^{2}+1\right )
\] |
[_quadrature] |
✓ |
0.327 |
|
|
\[
{}y^{2} = a^{2} \left ({y^{\prime }}^{2}+1\right )
\] |
[_quadrature] |
✓ |
1.181 |
|
|
\[
{}y^{2}+x y y^{\prime }-x^{2} {y^{\prime }}^{2} = 0
\] |
[_separable] |
✓ |
0.848 |
|
|
\[
{}y = y {y^{\prime }}^{2}+2 y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.908 |
|
|
\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.477 |
|
|
\[
{}x^{2} \left (y-y^{\prime } x \right ) = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.884 |
|
|
\[
{}y = y^{\prime } x +\arcsin \left (y^{\prime }\right )
\] |
[_Clairaut] |
✓ |
1.721 |
|
|
\[
{}{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.955 |
|
|
\[
{}x y \left (y-y^{\prime } x \right ) = x +y y^{\prime }
\] |
[_separable] |
✓ |
3.483 |
|
|
\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.797 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.030 |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.516 |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
[_separable] |
✓ |
76.803 |
|
|
\[
{}y = -y^{\prime } x +x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.861 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
1.391 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.913 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = a \left ({y^{\prime }}^{2}+1\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
44.212 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
10.826 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.456 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.903 |
|
|
\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left ({y^{\prime }}^{2}+1\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.974 |
|
|
\[
{}y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\] |
[_quadrature] |
✓ |
3.760 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
115.576 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.068 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
12.646 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {{y^{\prime }}^{2}+1}} = a
\] |
[_quadrature] |
✓ |
0.491 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
5.408 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
7.171 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
3.122 |
|
|
\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.933 |
|
|
\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
1.361 |
|
|
\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
15.368 |
|
|
\[
{}y-\frac {1}{\sqrt {{y^{\prime }}^{2}+1}} = b
\] |
[_quadrature] |
✓ |
1.565 |
|
|
\[
{}y = y^{\prime } x +\frac {m}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.381 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
106.115 |
|
|
\[
{}y = y^{\prime } x +a \sqrt {{y^{\prime }}^{2}+1}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
6.089 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.317 |
|
|
\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
[_separable] |
✓ |
9.083 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
73.075 |
|
|
\[
{}\left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
29.460 |
|
|
\[
{}y^{2} \left ({y^{\prime }}^{2}+1\right ) = r^{2}
\] |
[_quadrature] |
✓ |
4.362 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.278 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.359 |
|
|
\[
{}a {y^{\prime }}^{3} = 27 y
\] |
[_quadrature] |
✓ |
1.308 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.433 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.386 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.596 |
|
|
\[
{}y = y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.855 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.317 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.250 |
|
|
\[
{}4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.651 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}-b^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.645 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\] |
[_rational] |
✓ |
108.234 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.088 |
|
|
\[
{}y^{\prime \prime }-m^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.068 |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.085 |
|
|
\[
{}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.085 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.066 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.006 |
|
|
\[
{}y^{\prime \prime \prime \prime }-m^{2} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }-y = 2+5 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.278 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.350 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime \prime }+y = 3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime \prime }-y = \left ({\mathrm e}^{x}+1\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.154 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.370 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.116 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = x^{4}+2 x +1
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.597 |
|
|
\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.651 |
|
|
\[
{}y^{\prime \prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = x \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.684 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.814 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.748 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.723 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.522 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.491 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.252 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.112 |
|