|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
[_separable] |
✓ |
16.443 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.773 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
1.114 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.628 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
100.286 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
23.296 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.244 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y^{\prime } y\right )+\left (x +y^{\prime } y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.158 |
|
|
\[
{}\left (y^{\prime } y+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.658 |
|
|
\[
{}y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\] |
[_quadrature] |
✓ |
72.718 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y^{\prime } y\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
123.604 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.825 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
251.550 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
[_quadrature] |
✓ |
0.886 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
8.223 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
507.285 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+x^{2} y^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
2.549 |
|
|
\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
30.802 |
|
|
\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
unknown |
✓ |
31.026 |
|
|
\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
16.648 |
|
|
\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\] |
[_quadrature] |
✓ |
32.873 |
|
|
\[
{}y = x y^{\prime }+\frac {m}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.542 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
106.908 |
|
|
\[
{}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
9.283 |
|