|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\] |
[_quadrature] |
✓ |
1.849 |
|
|
\[
{}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
8.691 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.617 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.029 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
504.072 |
|
|
\[
{}{y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
100.839 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
35.214 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.671 |
|
|
\[
{}{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.116 |
|
|
\[
{}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\] |
[_quadrature] |
✓ |
142.629 |
|
|
\[
{}{y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.693 |
|
|
\[
{}{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
2.363 |
|
|
\[
{}{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.801 |
|
|
\[
{}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.323 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
3.356 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
3.204 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\] |
[_quadrature] |
✓ |
4.353 |
|
|
\[
{}2 {y^{\prime }}^{3}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.503 |
|
|
\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
68.356 |
|
|
\[
{}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
83.201 |
|
|
\[
{}4 {y^{\prime }}^{3}+4 y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.516 |
|
|
\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.739 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.752 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
2.771 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
135.987 |
|
|
\[
{}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.654 |
|
|
\[
{}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
1.000 |
|
|
\[
{}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.963 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.415 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\] |
[_quadrature] |
✓ |
0.591 |
|
|
\[
{}x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
530.461 |
|
|
\[
{}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
12.313 |
|
|
\[
{}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
127.410 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
11.642 |
|
|
\[
{}y {y^{\prime }}^{3}-3 y^{\prime } x +3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
7.372 |
|
|
\[
{}2 y {y^{\prime }}^{3}-3 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
1.521 |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
5.882 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
117.473 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.771 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
107.145 |
|
|
\[
{}16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
105.890 |
|
|
\[
{}x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
252.691 |
|
|
\[
{}y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
245.719 |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
109.256 |
|
|
\[
{}{y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2}
\] |
[_quadrature] |
✓ |
1.026 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.444 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.486 |
|
|
\[
{}{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.037 |
|
|
\[
{}{y^{\prime }}^{4}+y^{\prime } x -3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.151 |
|
|
\[
{}{y^{\prime }}^{4}-4 x^{2} y {y^{\prime }}^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.630 |
|
|
\[
{}{y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0
\] |
[_quadrature] |
✓ |
2.495 |
|
|
\[
{}2 {y^{\prime }}^{4}-y y^{\prime }-2 = 0
\] |
[_quadrature] |
✓ |
1.082 |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.268 |
|
|
\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.519 |
|
|
\[
{}{y^{\prime }}^{6} = \left (y-a \right )^{4} \left (y-b \right )^{3}
\] |
[_quadrature] |
✓ |
1.529 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.841 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.383 |
|
|
\[
{}{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
5.213 |
|
|
\[
{}x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2}
\] |
[_rational] |
✓ |
16.482 |
|
|
\[
{}2 \sqrt {a y^{\prime }}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
1.709 |
|
|
\[
{}\left (x -y\right ) \sqrt {y^{\prime }} = a \left (1+y^{\prime }\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.796 |
|
|
\[
{}2 \left (1+y\right )^{{3}/{2}}+3 y^{\prime } x -3 y = 0
\] |
[_separable] |
✓ |
4.987 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = x
\] |
[_quadrature] |
✓ |
1.050 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.703 |
|
|
\[
{}\sqrt {1+{y^{\prime }}^{2}} = y^{\prime } x
\] |
[_quadrature] |
✓ |
1.023 |
|
|
\[
{}\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
7.628 |
|
|
\[
{}a \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
6.301 |
|
|
\[
{}a x \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✗ |
317.821 |
|
|
\[
{}\sqrt {\left (a \,x^{2}+y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )}-y y^{\prime }-a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
78.633 |
|
|
\[
{}a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+y^{\prime } x -y = 0
\] |
[_Clairaut] |
✓ |
73.981 |
|
|
\[
{}\cos \left (y^{\prime }\right )+y^{\prime } x = y
\] |
[_Clairaut] |
✓ |
1.158 |
|
|
\[
{}a \cos \left (y^{\prime }\right )+b y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.485 |
|
|
\[
{}\sin \left (y^{\prime }\right )+y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.529 |
|
|
\[
{}y^{\prime } \sin \left (y^{\prime }\right )+\cos \left (y^{\prime }\right ) = y
\] |
[_quadrature] |
✓ |
34.034 |
|
|
\[
{}{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right ) = y
\] |
[_dAlembert] |
✓ |
1.535 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2} = 1
\] |
[_Clairaut] |
✓ |
7.965 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.151 |
|
|
\[
{}{\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
1.320 |
|
|
\[
{}\ln \left (y^{\prime }\right )+y^{\prime } x +a = 0
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}\ln \left (y^{\prime }\right )+y^{\prime } x +a = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.592 |
|
|
\[
{}\ln \left (y^{\prime }\right )+y^{\prime } x +a +b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.186 |
|
|
\[
{}\ln \left (y^{\prime }\right )+4 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.851 |
|
|
\[
{}\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.664 |
|
|
\[
{}a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.296 |
|
|
\[
{}y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-x y = 0
\] |
[_separable] |
✓ |
3.958 |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.048 |
|
|
\[
{}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y = 0
\] |
[_Clairaut] |
✓ |
11.863 |
|
|
\[
{}\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y
\] |
[_dAlembert] |
✓ |
0.378 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.469 |
|
|
\[
{}y^{\prime } = \frac {x +y-3}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.517 |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.010 |
|
|
\[
{}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
1.537 |
|
|
\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
[_Bernoulli] |
✓ |
1.249 |
|
|
\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.532 |
|
|
\[
{}y+x y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.211 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = R^{2}
\] |
[_quadrature] |
✓ |
4.911 |
|
|
\[
{}y = y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
[_Clairaut] |
✓ |
34.317 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.505 |
|
|
\[
{}\left (x +1\right ) y+x \left (1-y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.515 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.728 |
|