|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2} = 1-y^{2}
\] |
[_quadrature] |
✓ |
9.690 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2}-y^{2}
\] |
[_quadrature] |
✓ |
70.262 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{2}
\] |
[_quadrature] |
✓ |
3.604 |
|
|
\[
{}{y^{\prime }}^{2} = a +b y^{2}
\] |
[_quadrature] |
✓ |
8.957 |
|
|
\[
{}{y^{\prime }}^{2} = x^{2} y^{2}
\] |
[_separable] |
✓ |
5.888 |
|
|
\[
{}{y^{\prime }}^{2} = \left (-1+y\right ) y^{2}
\] |
[_quadrature] |
✓ |
77.381 |
|
|
\[
{}{y^{\prime }}^{2} = \left (y-a \right ) \left (y-b \right ) \left (y-c \right )
\] |
[_quadrature] |
✓ |
80.486 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{n}
\] |
[_quadrature] |
✓ |
39.431 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2}
\] |
[_quadrature] |
✓ |
14.379 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
98.243 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
63.657 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
98.301 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
98.543 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2}
\] |
[_separable] |
✓ |
83.621 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.355 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.224 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.372 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
0.544 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
0.581 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b = 0
\] |
[_quadrature] |
✓ |
0.361 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b x = 0
\] |
[_quadrature] |
✓ |
0.271 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b y = 0
\] |
[_quadrature] |
✓ |
0.733 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x +1 = 0
\] |
[_quadrature] |
✓ |
0.270 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.315 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.271 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.445 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x +x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.391 |
|
|
\[
{}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.467 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.324 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.342 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.336 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +1 = 0
\] |
[_quadrature] |
✓ |
0.263 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.308 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.357 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.294 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.277 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right ) = 0
\] |
[_quadrature] |
✓ |
0.270 |
|
|
\[
{}{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.394 |
|
|
\[
{}{y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.366 |
|
|
\[
{}{y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.329 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime } = b c \,x^{2}
\] |
[_quadrature] |
✓ |
0.246 |
|
|
\[
{}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.327 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.931 |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.447 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y^{\prime } x = 0
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.796 |
|
|
\[
{}{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.129 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.572 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
[_quadrature] |
✓ |
0.250 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime } = x \left (x +y\right )
\] |
[_quadrature] |
✓ |
1.317 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.101 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x = 0
\] |
[_quadrature] |
✓ |
0.480 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0
\] |
[_dAlembert] |
✓ |
42.126 |
|
|
\[
{}{y^{\prime }}^{2}+\left (1+2 y\right ) y^{\prime }+y \left (-1+y\right ) = 0
\] |
[_quadrature] |
✓ |
0.552 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x = 0
\] |
[_quadrature] |
✓ |
0.951 |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+4 y\right ) y^{\prime }+\left (1+4 y\right ) y = 0
\] |
[_quadrature] |
✓ |
0.977 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y = 0
\] |
[_quadrature] |
✓ |
1.197 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0
\] |
[_quadrature] |
✓ |
0.994 |
|
|
\[
{}{y^{\prime }}^{2}+a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
160.383 |
|
|
\[
{}{y^{\prime }}^{2}-a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
197.328 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
1.087 |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.850 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x = 0
\] |
[_quadrature] |
✓ |
1.324 |
|
|
\[
{}{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2} = 0
\] |
[_quadrature] |
✓ |
2.854 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
1.835 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
7.303 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.078 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
3.678 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.216 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
0.872 |
|
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.882 |
|
|
\[
{}{y^{\prime }}^{2} = {\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.678 |
|
|
\[
{}2 {y^{\prime }}^{2}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.407 |
|
|
\[
{}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.349 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.368 |
|
|
\[
{}2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0
\] |
[_quadrature] |
✓ |
2.852 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.373 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.099 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.198 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
9.972 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.734 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.394 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.363 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
264.806 |
|
|
\[
{}x {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.218 |
|
|
\[
{}x {y^{\prime }}^{2} = -x^{2}+a
\] |
[_quadrature] |
✓ |
0.363 |
|
|
\[
{}x {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.090 |
|
|
\[
{}x {y^{\prime }}^{2}+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.042 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } = y
\] |
[_rational, _dAlembert] |
✓ |
0.875 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.465 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.845 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.958 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.127 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.893 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.464 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.327 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.699 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
6.151 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.642 |
|