|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
2.072 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.320 |
|
|
\[
{}4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime } = 8 x^{3}-y^{2}
\] |
[_linear] |
✓ |
0.562 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (-a +1\right ) x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.275 |
|
|
\[
{}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
74.624 |
|
|
\[
{}x^{3} {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.263 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.888 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.456 |
|
|
\[
{}x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
10.993 |
|
|
\[
{}4 x \left (-x +a \right ) \left (b -x \right ) {y^{\prime }}^{2} = \left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2}
\] |
[_quadrature] |
✓ |
0.798 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.983 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.070 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.383 |
|
|
\[
{}x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y-y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.151 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.808 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.155 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.238 |
|
|
\[
{}y {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.624 |
|
|
\[
{}y {y^{\prime }}^{2} = a^{2} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.227 |
|
|
\[
{}y {y^{\prime }}^{2} = {\mathrm e}^{2 x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.320 |
|
|
\[
{}y {y^{\prime }}^{2}+2 a x y^{\prime }-a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.396 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.056 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.713 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.053 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.960 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
3.168 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.774 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
1.482 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
3.630 |
|
|
\[
{}y {y^{\prime }}^{2}+y = a
\] |
[_quadrature] |
✓ |
0.491 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.904 |
|
|
\[
{}\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.961 |
|
|
\[
{}2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.829 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.119 |
|
|
\[
{}\left (1-a y\right ) {y^{\prime }}^{2} = a y
\] |
[_quadrature] |
✓ |
1.007 |
|
|
\[
{}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.644 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
1.576 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (y^{2}+x^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
4.162 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
3.922 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
4.332 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
1473.682 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
[_rational] |
✓ |
171.316 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
4.305 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.301 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
72.194 |
|
|
\[
{}y^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
1.685 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-a^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
4.559 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.635 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.150 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
75.082 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
4.064 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
0.990 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
23.096 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.755 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
77.717 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (-a +1\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
9.357 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.600 |
|
|
\[
{}\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2}
\] |
[_quadrature] |
✓ |
0.898 |
|
|
\[
{}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
76.530 |
|
|
\[
{}\left (\left (-a +1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (-a +1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
311.661 |
|
|
\[
{}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
341.808 |
|
|
\[
{}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
168.690 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.720 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.802 |
|
|
\[
{}\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
21.116 |
|
|
\[
{}2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
141.877 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.576 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0
\] |
[_separable] |
✓ |
4.113 |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
17.116 |
|
|
\[
{}9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.601 |
|
|
\[
{}\left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.464 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
157.786 |
|
|
\[
{}\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+y^{2} a = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
10.479 |
|
|
\[
{}a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
28.197 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
10.733 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[_rational] |
✓ |
14.556 |
|
|
\[
{}2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
9.802 |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (y^{2}+x^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.218 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.313 |
|
|
\[
{}3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
52.020 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.246 |
|
|
\[
{}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
14.401 |
|
|
\[
{}{y^{\prime }}^{3} = b x +a
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{n}
\] |
[_quadrature] |
✓ |
0.457 |
|
|
\[
{}{y^{\prime }}^{3}+x -y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.622 |
|
|
\[
{}{y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.542 |
|
|
\[
{}{y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2}
\] |
[_quadrature] |
✓ |
1.016 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.374 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.872 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }+a -b x = 0
\] |
[_quadrature] |
✓ |
1.127 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.730 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.014 |
|
|
\[
{}{y^{\prime }}^{3}-7 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
1.232 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.654 |
|
|
\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.539 |
|
|
\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.519 |
|
|
\[
{}{y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\] |
[_quadrature] |
✓ |
0.617 |
|
|
\[
{}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.587 |
|
|
\[
{}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.612 |
|