| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.931 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.275 |
|
| \begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
x {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.191 |
|
| \begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.829 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.100 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-y x -y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.313 |
|
| \begin{align*}
{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| \begin{align*}
{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
{y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 1.096 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.423 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{3}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.787 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.121 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| \begin{align*}
{y^{\prime }}^{4}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.421 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y^{4} x^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.768 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-y^{2}+1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.224 |
|
| \begin{align*}
{y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.810 |
|
| \begin{align*}
{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
26.590 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.238 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
58.571 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.055 |
|
| \begin{align*}
{x^{\prime }}^{2}-t x+x&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 2.306 |
|
| \begin{align*}
x {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.283 |
|
| \begin{align*}
{\mathrm e}^{x} {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.077 |
|