|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-y^{\prime } x = 0
\] |
[_exact] |
✗ |
5.489 |
|
|
\[
{}f \left (x^{c} y\right ) \left (b x y^{\prime }-a \right )-x^{a} y^{b} \left (y^{\prime } x +c y\right ) = 0
\] |
[NONE] |
✗ |
2.626 |
|
|
\[
{}{y^{\prime }}^{2}+a y+b \,x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.335 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2}-a^{2} = 0
\] |
[_quadrature] |
✓ |
0.650 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2}-f \left (x \right )^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.673 |
|
|
\[
{}{y^{\prime }}^{2}-y^{3}+y^{2} = 0
\] |
[_quadrature] |
✓ |
1.970 |
|
|
\[
{}{y^{\prime }}^{2}-4 y^{3}+a y+b = 0
\] |
[_quadrature] |
✓ |
1.954 |
|
|
\[
{}{y^{\prime }}^{2}+a^{2} y^{2} \left (\ln \left (y\right )^{2}-1\right ) = 0
\] |
[_quadrature] |
✓ |
2.000 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.340 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b x = 0
\] |
[_quadrature] |
✓ |
0.193 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b y = 0
\] |
[_quadrature] |
✓ |
0.766 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.381 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.440 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.344 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.336 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.336 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c = 0
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.628 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.556 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.619 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.591 |
|
|
\[
{}{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.100 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0
\] |
[_dAlembert] |
✓ |
44.809 |
|
|
\[
{}{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y = 0
\] |
[_quadrature] |
✓ |
1.120 |
|
|
\[
{}{y^{\prime }}^{2}+a y y^{\prime }-b x -c = 0
\] |
[_dAlembert] |
✓ |
1.127 |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
0.597 |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.813 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.099 |
|
|
\[
{}{y^{\prime }}^{2}+2 f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
13.313 |
|
|
\[
{}{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
1.345 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.769 |
|
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.036 |
|
|
\[
{}2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.439 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.850 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.344 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 y^{\prime } x -y+x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.594 |
|
|
\[
{}a {y^{\prime }}^{2}+b y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.592 |
|
|
\[
{}a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.740 |
|
|
\[
{}a {y^{\prime }}^{2}+y y^{\prime }-x = 0
\] |
unknown |
✗ |
641.518 |
|
|
\[
{}a {y^{\prime }}^{2}-y y^{\prime }-x = 0
\] |
unknown |
✗ |
367.569 |
|
|
\[
{}x {y^{\prime }}^{2}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.394 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.828 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.877 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.993 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.786 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.397 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.337 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.355 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
16.448 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.728 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.352 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.677 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.642 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.478 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.263 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.507 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.649 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.019 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.549 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (2+y\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.536 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.584 |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.650 |
|
|
\[
{}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.712 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
[_rational, _dAlembert] |
✗ |
2.115 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{4}+y^{2} = 0
\] |
[_separable] |
✓ |
2.166 |
|
|
\[
{}\left (y^{\prime } x +a \right )^{2}-2 a y+x^{2} = 0
\] |
[_rational] |
✓ |
2.312 |
|
|
\[
{}\left (y^{\prime } x +y+2 x \right )^{2}-4 y x -4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.029 |
|
|
\[
{}y^{\prime }-1 = 0
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (1+y\right )-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.644 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.251 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 y x +a \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.645 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
2.742 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0
\] |
[_separable] |
✓ |
0.369 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
2.493 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (2+y\right ) y^{\prime }+4 y \left (2+y\right ) = 0
\] |
[_separable] |
✓ |
0.708 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
1.991 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
152.320 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
0.623 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.545 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.270 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.974 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
1.995 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
11.274 |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.952 |
|
|
\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
[_rational] |
✓ |
19.921 |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
74.396 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.208 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
6.017 |
|
|
\[
{}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
5.465 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.918 |
|
|
\[
{}x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.496 |
|
|
\[
{}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
8.622 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
6.984 |
|
|
\[
{}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
119.799 |
|
|
\[
{}y {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
2.063 |
|
|
\[
{}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.268 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.819 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.010 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.776 |
|
|
\[
{}y {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.427 |
|