| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.846 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +x^{2} {\mathrm e}^{\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.191 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.560 |
|
| \begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{-\frac {y}{x}} x}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.656 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.974 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.547 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\cosh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.877 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.150 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
y \left (6\right ) &= \pi \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.251 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.340 |
|
| \begin{align*}
y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.093 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.874 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✓ |
2.564 |
|
| \begin{align*}
-y+y^{\prime } x&=x \cot \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.433 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.079 |
|
| \begin{align*}
y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
2.633 |
|
| \begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} | [[_homogeneous, ‘class A‘], _dAlembert] | ✓ | ✓ | ✓ | ✗ | 5.361 |
|
| \begin{align*}
-y+y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.339 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (y-y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.733 |
|
| \begin{align*}
y^{\prime } x&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.297 |
|
| \begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.047 |
|
| \begin{align*}
y^{\prime } x -y+x \sec \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.007 |
|
| \begin{align*}
y^{\prime } x&=y+x \sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.289 |
|
| \begin{align*}
y^{\prime } x&=y+x \sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.749 |
|
| \begin{align*}
y^{\prime } x&=y-\tan \left (\frac {y}{x}\right ) x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.869 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.703 |
|
| \begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.065 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.744 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=y^{\prime } x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.744 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.809 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.043 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.467 |
|
| \begin{align*}
y^{\prime }&=\frac {t \sec \left (\frac {y}{t}\right )+y}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.842 |
|
| \begin{align*}
-y+y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x \\
\end{align*} | [[_homogeneous, ‘class A‘], _dAlembert] | ✓ | ✓ | ✓ | ✓ | 5.450 |
|
| \begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.298 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.777 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.137 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| \begin{align*}
y^{\prime }&=2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
3.796 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.280 |
|
| \begin{align*}
y^{\prime } x +\tan \left (\frac {y}{x}\right ) x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.745 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.655 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.382 |
|
| \begin{align*}
x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.938 |
|
| \begin{align*}
\tan \left (\frac {y}{x}\right ) x +y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.757 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.117 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right ) y^{\prime }&=y \cos \left (\frac {y}{x}\right )-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.100 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.143 |
|
| \begin{align*}
y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.636 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.379 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.281 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.257 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} | [[_homogeneous, ‘class A‘], _dAlembert] | ✓ | ✓ | ✓ | ✓ | 3.753 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=\sin \left (\frac {y}{x}\right ) y-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.085 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\csc \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
118.658 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
4.063 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.851 |
|
| \begin{align*}
-y+y^{\prime } x&=\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
3.239 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.764 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y}{x}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.858 |
|
| \begin{align*}
-y+y^{\prime } x&=x \cos \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.086 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}}-\frac {y}{x}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.092 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.982 |
|
| \begin{align*}
x \csc \left (\frac {y}{x}\right )-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.738 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (y-y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.522 |
|
| \begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
96.438 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.861 |
|