| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }&=f \left (y\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.199 |
|
| \begin{align*}
g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.785 |
|
| \begin{align*}
f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.140 |
|
| \begin{align*}
\left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
✗ |
1.036 |
|
| \begin{align*}
\left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
9.973 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }+y^{n}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
7.776 |
|
| \begin{align*}
2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.465 |
|
| \begin{align*}
3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.337 |
|
| \begin{align*}
\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.868 |
|
| \begin{align*}
a y \left (-1+y\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
6.077 |
|
| \begin{align*}
h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.725 |
|
| \begin{align*}
y^{\prime \prime }-f \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.266 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
3.850 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
3.141 |
|
| \begin{align*}
m x^{\prime \prime }&=f \left (x\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.754 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
4.035 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \left (2+y^{\prime } x -4 y^{2} y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✗ |
✗ |
0.967 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
7.689 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{6}\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✗ |
✗ |
✗ |
5.621 |
|