|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y-x^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.625 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.509 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
16.259 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.682 |
|
|
\[
{}x {y^{\prime }}^{2}-y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.438 |
|
|
\[
{}x {y^{\prime }}^{2}-y^{\prime } y+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.836 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y^{\prime } y-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.638 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.512 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.399 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.529 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.726 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.043 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.572 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.562 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.613 |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.681 |
|
|
\[
{}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.734 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
[_rational, _dAlembert] |
✗ |
2.105 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{4}+y^{2} = 0
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}\left (x y^{\prime }+a \right )^{2}-2 a y+x^{2} = 0
\] |
[_rational] |
✓ |
86.158 |
|
|
\[
{}\left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.301 |
|
|
\[
{}y^{\prime }-1 = 0
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.458 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.166 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+a \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.682 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
3.073 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0
\] |
[_separable] |
✓ |
0.410 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
2.727 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right ) = 0
\] |
[_separable] |
✓ |
0.740 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
2.193 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
150.385 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
1.040 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.580 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.016 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
2.084 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
27.272 |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.982 |
|
|
\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
[_rational] |
✓ |
69.406 |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
73.875 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.248 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.615 |
|
|
\[
{}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
11.103 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.932 |
|
|
\[
{}x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
15.749 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
25.607 |
|
|
\[
{}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
262.454 |
|
|
\[
{}y {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.677 |
|
|
\[
{}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.345 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.075 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.126 |
|
|
\[
{}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.978 |
|
|
\[
{}y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.592 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.150 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.786 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.039 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
3.297 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.947 |
|
|
\[
{}\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.977 |
|
|
\[
{}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.970 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.854 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.152 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.971 |
|
|
\[
{}\left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0
\] |
[_quadrature] |
✓ |
0.961 |
|
|
\[
{}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\] |
[_rational, _dAlembert] |
✓ |
419.532 |
|
|
\[
{}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\] |
[_rational] |
✓ |
3.354 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
4.256 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
19.291 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.469 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
72.466 |
|
|
\[
{}a x y {y^{\prime }}^{2}-\left (y^{2} a +b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
1794.732 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0
\] |
[_quadrature] |
✓ |
4.722 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.204 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
75.586 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} a +b x +c = 0
\] |
[_rational] |
✓ |
8.560 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
78.765 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-a +1\right ) y^{2}+a \,x^{2}+\left (a -1\right ) b = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
9.908 |
|
|
\[
{}\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.936 |
|
|
\[
{}\left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
88.875 |
|
|
\[
{}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.964 |
|
|
\[
{}\left (y^{2}+\left (-a +1\right ) x^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-a +1\right ) y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
317.210 |
|
|
\[
{}\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
21.971 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.704 |
|
|
\[
{}\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.181 |
|
|
\[
{}\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }+y^{2} a -b \,x^{2}-a b = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
10.973 |
|
|
\[
{}\left (y^{2} a +b x +c \right ) {y^{\prime }}^{2}-b y y^{\prime }+d y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
88.784 |
|
|
\[
{}\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
31.773 |
|
|
\[
{}\left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
466.747 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-\left (y^{3}+x^{3}-a \right ) y^{\prime }+x^{2} y = 0
\] |
[_rational] |
✓ |
14.830 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3} = 0
\] |
[_separable] |
✓ |
74.629 |
|
|
\[
{}x^{2} \left (-1+x y^{2}\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (y-x \right ) y^{\prime }-y^{2} \left (x^{2} y-1\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
28.098 |
|
|
\[
{}\left (y^{4}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+y^{2} \left (y^{2}-a^{2}\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
25.556 |
|
|
\[
{}\left (y^{4}+x^{2} y^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
11.970 |
|
|
\[
{}9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
14.901 |
|
|
\[
{}x^{2} \left (x^{2} y^{4}-1\right ) {y^{\prime }}^{2}+2 x^{3} y^{3} \left (y^{2}-x^{2}\right ) y^{\prime }-y^{2} \left (x^{4} y^{2}-1\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
30.517 |
|
|
\[
{}\left (a^{2} \sqrt {y^{2}+x^{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a^{2} \sqrt {y^{2}+x^{2}}-y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
150.368 |
|
|
\[
{}\left (a \left (y^{2}+x^{2}\right )^{{3}/{2}}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+a \left (y^{2}+x^{2}\right )^{{3}/{2}}-y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
44.255 |
|
|
\[
{}{y^{\prime }}^{2} \sin \left (y\right )+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
145.789 |
|