|
# |
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]] |
✓ |
4.288 |
|
|
\[
{}2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.545 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.216 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.574 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.989 |
|
|
\[
{}a {y^{\prime }}^{2}+b y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.672 |
|
|
\[
{}a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.432 |
|
|
\[
{}a {y^{\prime }}^{2}+y y^{\prime }-x = 0
\] |
[_dAlembert] |
✓ |
109.660 |
|
|
\[
{}a {y^{\prime }}^{2}-y y^{\prime }-x = 0
\] |
[_dAlembert] |
✓ |
96.954 |
|
|
\[
{}x {y^{\prime }}^{2}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.227 |
|
|
\[
{}x {y^{\prime }}^{2}+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.116 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.251 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.436 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.312 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.636 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.937 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.673 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.425 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-3 x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.194 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.578 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.995 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.505 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.637 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.139 |
|
|
\[
{}4 x -2 y y^{\prime }+x {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.689 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.010 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.707 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.735 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.686 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.724 |
|
|
\[
{}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.910 |
|
|
\[
{}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.960 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0
\] |
[_dAlembert] |
✓ |
1.419 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
2.858 |
|
|
\[
{}\left (y^{\prime } x +a \right )^{2}-2 a y+x^{2} = 0
\] |
[_rational] |
✗ |
72.477 |
|
|
\[
{}\left (y^{\prime } x +y+2 x \right )^{2}-4 x y-4 x^{2}-4 a = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.863 |
|
|
\[
{}y^{\prime }-1 = 0
\] |
[_quadrature] |
✓ |
0.634 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x +y \left (1+y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.549 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
9.937 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.857 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2} = 0
\] |
[_separable] |
✓ |
0.751 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+3 y^{2} = 0
\] |
[_separable] |
✓ |
0.534 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y-5 y^{2} = 0
\] |
[_separable] |
✓ |
0.773 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0
\] |
[_separable] |
✓ |
0.666 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (x^{2} y-2 x y+x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right ) = 0
\] |
[_linear] |
✓ |
0.657 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y \left (y-2 x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
76.055 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a \,x^{2} y^{3}+b \right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
5.036 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.796 |
|
|
\[
{}{y^{\prime }}^{2} \left (x^{2}-1\right )-1 = 0
\] |
[_quadrature] |
✓ |
0.514 |
|
|
\[
{}{y^{\prime }}^{2} \left (x^{2}-1\right )-y^{2}+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.449 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+y^{2} = 0
\] |
[_separable] |
✓ |
0.652 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
33.105 |
|
|
\[
{}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.009 |
|
|
\[
{}\left (2 x^{2}+1\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x y+x^{2}+2\right ) y^{\prime }+2 y^{2}+1 = 0
\] |
[_rational] |
✗ |
71.454 |
|
|
\[
{}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y^{\prime } y-y^{2}+a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
138.308 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.325 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.103 |
|
|
\[
{}x \left (x^{2}-1\right ) {y^{\prime }}^{2}+2 \left (-x^{2}+1\right ) y y^{\prime }+x y^{2}-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
12.676 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.956 |
|
|
\[
{}x^{2} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.805 |
|
|
\[
{}{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
21.022 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) \cos \left (x \right )^{4}-a^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
28.288 |
|
|
\[
{}y {y^{\prime }}^{2}-1 = 0
\] |
[_quadrature] |
✓ |
0.519 |
|
|
\[
{}y {y^{\prime }}^{2}-{\mathrm e}^{2 x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.302 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.936 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -9 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.498 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.157 |
|
|
\[
{}y {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.981 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.381 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.186 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.957 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y-x \right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.061 |
|
|
\[
{}\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.998 |
|
|
\[
{}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.912 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.738 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.071 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.995 |
|
|
\[
{}\left (b +a y\right ) \left (1+{y^{\prime }}^{2}\right )-c = 0
\] |
[_quadrature] |
✓ |
0.860 |
|
|
\[
{}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0
\] |
[_rational, _dAlembert] |
✓ |
539.148 |
|
|
\[
{}\left (a y-x^{2}\right ) {y^{\prime }}^{2}+2 x y {y^{\prime }}^{2}-y^{2} = 0
\] |
[_rational] |
✗ |
3.638 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
0.978 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0
\] |
[_rational] |
✗ |
38.759 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.802 |
|
|
\[
{}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y^{\prime } y-y^{2}+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
164.600 |
|
|
\[
{}a x y {y^{\prime }}^{2}-\left (a y^{2}+b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
187.318 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-a^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.690 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.468 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
74.439 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y^{\prime } y+a y^{2}+b x +c = 0
\] |
[_rational] |
✗ |
9.589 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y^{\prime } y+a -x^{2}+2 y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
84.166 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
11.050 |
|
|
\[
{}\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.869 |
|
|
\[
{}\left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
81.734 |
|
|
\[
{}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+\left (-a^{2}+1\right ) x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.556 |
|
|
\[
{}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
507.420 |
|
|
\[
{}\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
15.195 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x^{2}+4 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.679 |
|
|
\[
{}\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y = 0
\] |
[_quadrature] |
✓ |
0.873 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.124 |
|