|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
16.647 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.418 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
1.148 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.456 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.900 |
|
|
\[
{}x {y^{\prime }}^{2}+a +b x -y-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.961 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.457 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.415 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.122 |
|
|
\[
{}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
12.145 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
3.653 |
|
|
\[
{}x {y^{\prime }}^{2}-a y y^{\prime }+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.603 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.923 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.216 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x \right ) y y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
3.618 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
2.355 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.551 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.477 |
|
|
\[
{}\left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.451 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.800 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.557 |
|
|
\[
{}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (2+y\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.209 |
|
|
\[
{}\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y = 0
\] |
[_rational, _dAlembert] |
✓ |
2.967 |
|
|
\[
{}4 x {y^{\prime }}^{2} = \left (a -3 x \right )^{2}
\] |
[_quadrature] |
✓ |
0.256 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.133 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.429 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.415 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
22.937 |
|
|
\[
{}4 \left (2-x \right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.207 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
7.838 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
1.197 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
5.220 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.901 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
6.915 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
4.482 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
5.117 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y = 0
\] |
[_rational] |
✓ |
3.544 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (1+y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
8.879 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
7.158 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.490 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.782 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.676 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 x \left (y+2 x \right ) y^{\prime }-4 a +y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
8.668 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
8.436 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
6.936 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+x^{3}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
165.345 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
4.444 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (2+y\right ) y^{\prime }+4 \left (2+y\right ) y = 0
\] |
[_separable] |
✓ |
0.748 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
3.951 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\] |
[_rational] |
✓ |
10.516 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (y+2 x \right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
213.921 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
193.234 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
0.847 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.141 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
12.701 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.502 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2} = 0
\] |
[_quadrature] |
✓ |
0.281 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = x^{2}
\] |
[_quadrature] |
✓ |
0.248 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
16.367 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
4.540 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.716 |
|
|
\[
{}4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime } = 8 x^{3}-y^{2}
\] |
[_linear] |
✓ |
1.808 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.147 |
|
|
\[
{}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
79.413 |
|
|
\[
{}x^{3} {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.231 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.235 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
10.901 |
|
|
\[
{}x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
7.396 |
|
|
\[
{}4 x \left (a -x \right ) \left (b -x \right ) {y^{\prime }}^{2} = \left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2}
\] |
[_quadrature] |
✓ |
0.781 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.174 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.736 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
8.196 |
|
|
\[
{}x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-y x -y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.023 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
13.608 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.571 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.707 |
|
|
\[
{}y {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
23.916 |
|
|
\[
{}y {y^{\prime }}^{2} = a^{2} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.241 |
|
|
\[
{}y {y^{\prime }}^{2} = {\mathrm e}^{2 x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.981 |
|
|
\[
{}y {y^{\prime }}^{2}+2 a x y^{\prime }-a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.410 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.105 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.775 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
2.884 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
8.436 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
9.332 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.097 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.490 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
9.706 |
|
|
\[
{}y {y^{\prime }}^{2}+y = a
\] |
[_quadrature] |
✓ |
1.155 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.321 |
|
|
\[
{}\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.750 |
|
|
\[
{}2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.086 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
8.662 |
|
|
\[
{}\left (1-a y\right ) {y^{\prime }}^{2} = a y
\] |
[_quadrature] |
✓ |
1.256 |
|
|
\[
{}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
3.882 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.510 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
10.632 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x = 0
\] |
[_separable] |
✓ |
10.491 |
|