| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 (i) |
\begin{align*}
x^{\prime }&=3 t^{2}+4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1 (ii) |
\begin{align*}
x^{\prime }&=b \,{\mathrm e}^{t} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1 (iii) |
\begin{align*}
x^{\prime }&=\frac {1}{t^{2}+1} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1 (iv) |
\begin{align*}
x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1 (v) |
\begin{align*}
x^{\prime }&=\cos \left (t \right ) \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 1 (vi) |
\begin{align*}
x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 (i) |
\begin{align*}
x^{\prime }&=x^{2}-3 x+2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 (ii) |
\begin{align*}
x^{\prime }&=b \,{\mathrm e}^{x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 (iii) |
\begin{align*}
x^{\prime }&=\left (x-1\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 (iv) |
\begin{align*}
x^{\prime }&=\sqrt {x^{2}-1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 (v) |
\begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
|
| 2 (vi) |
\begin{align*}
x^{\prime }&=\tan \left (x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (i) |
\begin{align*}
3 x t^{2}-x t +\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (ii) |
\begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (iii) |
\begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (iv) |
\begin{align*}
\left (t^{2}-x^{2}\right ) x^{\prime }&=x t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (v) |
\begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 (vi) | \begin{align*}
2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
|
| 4 (i) |
\begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 (ii) |
\begin{align*}
x^{\prime }+x \tan \left (t \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 (iii) |
\begin{align*}
x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 (iv) |
\begin{align*}
t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 (v) |
\begin{align*}
x^{\prime }+2 x t +t x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 4 (vi) |
\begin{align*}
x^{\prime } t +x \ln \left (t \right )&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 |
\begin{align*}
x^{\prime } t +x g \left (t \right )&=h \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 |
\begin{align*}
t^{2} x^{\prime \prime }-6 x^{\prime } t +12 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1 |
\begin{align*}
x^{\prime }&=-\lambda x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 2 |
\begin{align*}
x^{\prime }\left (t \right )&=x \left (t \right ) \\
y^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 3 |
\begin{align*}
t^{2} x^{\prime \prime }-2 x^{\prime } t +2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 (i) |
\begin{align*}
x^{\prime \prime }-5 x^{\prime }+6 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 (ii) |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 (iiI=i) |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 5 (iv) |
\begin{align*}
x^{\prime \prime }+3 x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 (i) |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 (ii) |
\begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 (iii) |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 6 (iv) |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 7 (i) |
\begin{align*}
x^{\prime \prime }-x&=t^{2} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 (ii) |
\begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 (iii) |
\begin{align*}
x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 (iv) |
\begin{align*}
x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 (v) |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=t \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|
| 7 (vi) |
\begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
|