| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1. Using series method |
\begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
|
| 1. direct method |
\begin{align*}
y^{\prime }&=y^{2}-x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2. Using series method |
\begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
|
| 2. direct method |
\begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3. series method |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✗ |
✓ |
|
| 3. direct method |
\begin{align*}
y^{\prime }&=y+x \,{\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
|