|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y = 0
\] |
[_quadrature] |
✓ |
1.090 |
|
|
\[
{}{y^{\prime }}^{2}+a y y^{\prime }-b x -c = 0
\] |
[_dAlembert] |
✓ |
4.293 |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.449 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.184 |
|
|
\[
{}{y^{\prime }}^{2}+2 f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
20.405 |
|
|
\[
{}{y^{\prime }}^{2}+y \left (y-x \right ) y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
0.638 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.845 |
|
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.737 |
|
|
\[
{}2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.405 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.749 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
4.011 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 y^{\prime } x -y+x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.617 |
|
|
\[
{}a {y^{\prime }}^{2}+b y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.619 |
|
|
\[
{}a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.265 |
|
|
\[
{}a {y^{\prime }}^{2}+y^{\prime } y-x = 0
\] |
[_dAlembert] |
✗ |
690.047 |
|
|
\[
{}a {y^{\prime }}^{2}-y^{\prime } y-x = 0
\] |
[_dAlembert] |
✗ |
329.543 |
|
|
\[
{}x {y^{\prime }}^{2}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.399 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.926 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
50.159 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
56.006 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.794 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
2.690 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y-x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.639 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.539 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } y-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
14.303 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.662 |
|
|
\[
{}x {y^{\prime }}^{2}-y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.385 |
|
|
\[
{}x {y^{\prime }}^{2}-y^{\prime } y+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.743 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y^{\prime } y-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.657 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
2.612 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.398 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.562 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime } y+2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.766 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.830 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.598 |
|
|
\[
{}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (2+y\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.632 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.625 |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_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] |
✓ |
0.760 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
[_rational, _dAlembert] |
✗ |
2.043 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{4}+y^{2} = 0
\] |
[_separable] |
✓ |
2.206 |
|
|
\[
{}\left (y^{\prime } x +a \right )^{2}-2 a y+x^{2} = 0
\] |
[_rational] |
✓ |
81.773 |
|
|
\[
{}\left (y^{\prime } x +y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
74.479 |
|
|
\[
{}y^{\prime }-1 = 0
\] |
[_quadrature] |
✓ |
0.759 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (1+y\right )-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
4.036 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.647 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+a \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.616 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
1.194 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0
\] |
[_separable] |
✓ |
0.492 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
0.984 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (2+y\right ) y^{\prime }+4 y \left (2+y\right ) = 0
\] |
[_separable] |
✓ |
0.766 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
0.808 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
74.256 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
0.641 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.577 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.311 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.020 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
0.828 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
16.312 |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.674 |
|
|
\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
69.529 |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
72.530 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.013 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.480 |
|
|
\[
{}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
11.078 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.019 |
|
|
\[
{}x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.558 |
|
|
\[
{}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
15.191 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
25.712 |
|
|
\[
{}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
264.429 |
|
|
\[
{}y {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.658 |
|
|
\[
{}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.852 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.475 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.888 |
|
|
\[
{}y {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.443 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.537 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.536 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.078 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
0.580 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.960 |
|
|
\[
{}\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.905 |
|
|
\[
{}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.879 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.771 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.082 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.906 |
|
|
\[
{}\left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0
\] |
[_quadrature] |
✓ |
0.935 |
|
|
\[
{}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\] |
[_rational, _dAlembert] |
✓ |
1162.676 |
|
|
\[
{}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\] |
[_rational] |
✓ |
3.329 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.520 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
18.484 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.078 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
72.046 |
|
|
\[
{}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
153.404 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0
\] |
[_quadrature] |
✓ |
4.544 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.099 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
73.088 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c = 0
\] |
[_rational] |
✓ |
8.326 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
77.519 |
|