|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
0.917 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.855 |
|
|
\[
{}4 x^{2} {y^{\prime }}^{2}-4 x y y^{\prime } = 8 x^{3}-y^{2}
\] |
[_linear] |
✓ |
0.531 |
|
|
\[
{}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.658 |
|
|
\[
{}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
71.651 |
|
|
\[
{}x^{3} {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.335 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.229 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.262 |
|
|
\[
{}x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.957 |
|
|
\[
{}4 x \left (-x +a \right ) \left (b -x \right ) {y^{\prime }}^{2} = \left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2}
\] |
[_quadrature] |
✓ |
1.055 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.912 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.254 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.961 |
|
|
\[
{}x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y-y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.028 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.053 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.846 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.959 |
|
|
\[
{}y {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}y {y^{\prime }}^{2} = a^{2} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.536 |
|
|
\[
{}y {y^{\prime }}^{2} = {\mathrm e}^{2 x}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.169 |
|
|
\[
{}y {y^{\prime }}^{2}+2 a x y^{\prime }-a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.865 |
|
|
\[
{}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.943 |
|
|
\[
{}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.574 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.461 |
|
|
\[
{}y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.905 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
0.549 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.900 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (1+x y\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.436 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.630 |
|
|
\[
{}y {y^{\prime }}^{2}+y = a
\] |
[_quadrature] |
✓ |
0.689 |
|
|
\[
{}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.790 |
|
|
\[
{}\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.804 |
|
|
\[
{}2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.764 |
|
|
\[
{}9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.119 |
|
|
\[
{}\left (1-a y\right ) {y^{\prime }}^{2} = a y
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.834 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.494 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.467 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
1.208 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_separable] |
✓ |
1.342 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
141.127 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
[_rational] |
✓ |
101.730 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 x y = 0
\] |
[_separable] |
✓ |
1.424 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
150.813 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
72.950 |
|
|
\[
{}y^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
0.651 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-a^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.476 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.993 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
72.300 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.616 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
0.720 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
31.248 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
13.391 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
80.392 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
10.843 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
30.265 |
|
|
\[
{}\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2}
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}\left (a^{2}-2 y a x +y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
84.885 |
|
|
\[
{}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
305.651 |
|
|
\[
{}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
340.019 |
|
|
\[
{}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
191.463 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.783 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.844 |
|
|
\[
{}\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
7.540 |
|
|
\[
{}2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
143.572 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.462 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3} = 0
\] |
[_separable] |
✓ |
0.887 |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.924 |
|
|
\[
{}9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.488 |
|
|
\[
{}\left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.398 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
327.426 |
|
|
\[
{}\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
11.929 |
|
|
\[
{}a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
8.647 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.966 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[_rational] |
✓ |
18.773 |
|
|
\[
{}2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.247 |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
150.332 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.559 |
|
|
\[
{}3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.509 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.444 |
|
|
\[
{}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
16.871 |
|
|
\[
{}{y^{\prime }}^{3} = b x +a
\] |
[_quadrature] |
✓ |
0.406 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{n}
\] |
[_quadrature] |
✓ |
0.529 |
|
|
\[
{}{y^{\prime }}^{3}+x -y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.473 |
|
|
\[
{}{y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.311 |
|
|
\[
{}{y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2}
\] |
[_quadrature] |
✓ |
6.161 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.569 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.332 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }+a -b x = 0
\] |
[_quadrature] |
✓ |
0.809 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
0.687 |
|
|
\[
{}{y^{\prime }}^{3}-7 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
0.705 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.685 |
|
|
\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.469 |
|
|
\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.441 |
|
|
\[
{}{y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\] |
[_quadrature] |
✓ |
0.779 |
|
|
\[
{}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.503 |
|
|
\[
{}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.511 |
|