|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.338 |
|
|
\[
{}2 {y^{\prime }}^{2}+\left (-1+x \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.432 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.174 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.423 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 x y^{\prime }-y+x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.754 |
|
|
\[
{}a {y^{\prime }}^{2}+b y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.996 |
|
|
\[
{}a {y^{\prime }}^{2}+y y^{\prime }-x = 0
\] |
[_dAlembert] |
✓ |
73.217 |
|
|
\[
{}a {y^{\prime }}^{2}-y y^{\prime }-x = 0
\] |
[_dAlembert] |
✓ |
46.317 |
|
|
\[
{}x {y^{\prime }}^{2}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.414 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.867 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.972 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.154 |
|
|
\[
{}x {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.785 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.490 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.773 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.249 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.469 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.831 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.432 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.375 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.276 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.490 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
0.950 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.338 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+2 y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.584 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.453 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.617 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.616 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.654 |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.713 |
|
|
\[
{}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.815 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
[_rational, _dAlembert] |
✓ |
1.532 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{4}+y^{2} = 0
\] |
[_separable] |
✓ |
2.746 |
|
|
\[
{}\left (x y^{\prime }+a \right )^{2}-2 a y+x^{2} = 0
\] |
[_rational] |
✓ |
70.193 |
|
|
\[
{}\left (x y^{\prime }+y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.450 |
|
|
\[
{}y^{\prime }-1 = 0
\] |
[_quadrature] |
✓ |
0.784 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y \left (y+1\right )-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.437 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )-x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.569 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+a \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.713 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
1.049 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+3 y^{2} = 0
\] |
[_separable] |
✓ |
0.461 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
0.942 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right ) = 0
\] |
[_separable] |
✓ |
0.474 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
0.805 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
70.548 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
7.958 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.634 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.343 |
|
|
\[
{}\left (x^{2}-1\right ) {y^{\prime }}^{2}-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.024 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
0.855 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
31.458 |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.726 |
|
|
\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
70.017 |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
69.131 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.524 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.999 |
|
|
\[
{}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.290 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.714 |
|
|
\[
{}x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
17.540 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
28.306 |
|
|
\[
{}y {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.364 |
|
|
\[
{}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.171 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.636 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.747 |
|
|
\[
{}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.617 |
|
|
\[
{}y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.578 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.858 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.500 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.768 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.696 |
|
|
\[
{}\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (-1+x \right ) y^{\prime }+y-2 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.763 |
|
|
\[
{}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.769 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.493 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.802 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.858 |
|
|
\[
{}\left (a y+b \right ) \left (1+{y^{\prime }}^{2}\right )-c = 0
\] |
[_quadrature] |
✓ |
0.552 |
|
|
\[
{}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\] |
[_rational, _dAlembert] |
✓ |
282.755 |
|
|
\[
{}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\] |
[_rational] |
✓ |
3.678 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.369 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
37.145 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
147.797 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
73.017 |
|
|
\[
{}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
56.085 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+y^{2}-a^{2} = 0
\] |
[_quadrature] |
✓ |
0.512 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.861 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+y^{2}-4 a x +4 a^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
72.013 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a y^{2}+b x +c = 0
\] |
[_rational] |
✓ |
9.119 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2}+a = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
79.845 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+a \,x^{2}+\left (a -1\right ) b = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
10.167 |
|
|
\[
{}\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.647 |
|
|
\[
{}\left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
78.706 |
|
|
\[
{}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.653 |
|
|
\[
{}\left (y^{2}+\left (1-a \right ) x^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (1-a \right ) y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
310.007 |
|
|
\[
{}\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
7.282 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.274 |
|
|
\[
{}\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0
\] |
[_quadrature] |
✓ |
0.615 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
292.509 |
|