|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\] |
[_quadrature] |
✓ |
69.619 |
|
|
\[
{}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
11.060 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
13.577 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y+3 x} \left (y^{\prime }-1\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.091 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{-2 y+3 x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
535.176 |
|
|
\[
{}{y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
0.356 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.892 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.594 |
|
|
\[
{}{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.940 |
|
|
\[
{}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\] |
[_quadrature] |
✓ |
0.496 |
|
|
\[
{}{y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.912 |
|
|
\[
{}{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
69.135 |
|
|
\[
{}{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.323 |
|
|
\[
{}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.412 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
1.289 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+x y \left (y^{2}+x y+x^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
1.133 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\] |
[_quadrature] |
✓ |
1.283 |
|
|
\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.453 |
|
|
\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
0.356 |
|
|
\[
{}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
81.847 |
|
|
\[
{}4 {y^{\prime }}^{3}+4 y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.575 |
|
|
\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.506 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.758 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.854 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
144.145 |
|
|
\[
{}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.584 |
|
|
\[
{}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.794 |
|
|
\[
{}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.829 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.641 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\] |
[_quadrature] |
✓ |
0.966 |
|
|
\[
{}x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
529.010 |
|
|
\[
{}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
15.836 |
|
|
\[
{}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
12.694 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
14.008 |
|
|
\[
{}y {y^{\prime }}^{3}-3 x y^{\prime }+3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.879 |
|
|
\[
{}2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.943 |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.974 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
109.957 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
108.366 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
110.951 |
|
|
\[
{}16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.526 |
|
|
\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
264.998 |
|
|
\[
{}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
248.490 |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
109.148 |
|
|
\[
{}{y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2}
\] |
[_quadrature] |
✓ |
2.066 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.638 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.152 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.676 |
|
|
\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.520 |
|
|
\[
{}{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.690 |
|
|
\[
{}{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0
\] |
[_quadrature] |
✓ |
6.162 |
|
|
\[
{}2 {y^{\prime }}^{4}-y y^{\prime }-2 = 0
\] |
[_quadrature] |
✓ |
1.505 |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.270 |
|
|
\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
1.013 |
|
|
\[
{}{y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3}
\] |
[_quadrature] |
✓ |
4.905 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
50.371 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
72.280 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
73.719 |
|
|
\[
{}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\] |
[_rational] |
✓ |
18.671 |
|
|
\[
{}2 \sqrt {a y^{\prime }}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
2.607 |
|
|
\[
{}\left (x -y\right ) \sqrt {y^{\prime }} = a \left (y^{\prime }+1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.189 |
|
|
\[
{}2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y = 0
\] |
[_separable] |
✓ |
3.163 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = x
\] |
[_quadrature] |
✓ |
1.220 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = y
\] |
[_quadrature] |
✓ |
2.134 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}} = x y^{\prime }
\] |
[_quadrature] |
✓ |
1.207 |
|
|
\[
{}\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
3.181 |
|
|
\[
{}a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.661 |
|
|
\[
{}a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
32.357 |
|
|
\[
{}\sqrt {\left (a \,x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )}-y y^{\prime }-a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
76.345 |
|
|
\[
{}a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+x y^{\prime }-y = 0
\] |
[_Clairaut] |
✓ |
18.524 |
|
|
\[
{}\cos \left (y^{\prime }\right )+x y^{\prime } = y
\] |
[_Clairaut] |
✓ |
1.275 |
|
|
\[
{}a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.554 |
|
|
\[
{}\sin \left (y^{\prime }\right )+y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.622 |
|
|
\[
{}y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y
\] |
[_quadrature] |
✓ |
71.092 |
|
|
\[
{}{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right ) = y
\] |
[_dAlembert] |
✓ |
1.816 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+x y^{\prime }\right )^{2} = 1
\] |
[_Clairaut] |
✓ |
9.768 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.217 |
|
|
\[
{}{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
2.141 |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a = 0
\] |
[_quadrature] |
✓ |
0.889 |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.720 |
|
|
\[
{}\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
4.734 |
|
|
\[
{}\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.139 |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.842 |
|
|
\[
{}a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.575 |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
2.963 |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.272 |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0
\] |
[_Clairaut] |
✗ |
115.828 |
|
|
\[
{}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y
\] |
[_dAlembert] |
✗ |
0.150 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
18.483 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.151 |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.092 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
1.634 |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
1.500 |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
35.648 |
|
|
\[
{}y+x y^{2}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.494 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = R^{2}
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y = x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
[_Clairaut] |
✓ |
9.020 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.528 |
|
|
\[
{}\left (x +1\right ) y+\left (1-y\right ) x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.517 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.715 |
|