| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| 1(a) |
\begin{align*}
y^{\prime } y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 1(b) |
\begin{align*}
y^{\prime }-y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 1(c) |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 1(d) |
\begin{align*}
y^{\prime }+y \cot \left (x \right )&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 1(e) |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 1(f) |
\begin{align*}
y^{\prime }+y \ln \left (x \right )&=x^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 2(a) |
\begin{align*}
y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 2(b) |
\begin{align*}
-y+y^{\prime } x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 2(c) |
\begin{align*}
y^{\prime } x +n y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 2(d) |
\begin{align*}
y^{\prime } x -n y&=x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 2(e) |
\begin{align*}
\left (x^{3}+x \right ) y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 3(a) |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 3(b) |
\begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 3(c) |
\begin{align*}
\tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 3(a) |
\begin{align*}
\tan \left (x \right ) y^{\prime }&=-\cos \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
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| 4(a) |
\begin{align*}
y^{\prime }+y \cos \left (x \right )&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
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| 4(b) |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
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| 4(c) | \begin{align*}
y^{\prime }+y \sin \left (x \right )&=\sin \left (2 x \right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✗ |
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| 4(d) |
\begin{align*}
\sin \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 5(a) |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }+y&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
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| 5(b) |
\begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
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| 5(c) |
\begin{align*}
\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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| 5(d) |
\begin{align*}
\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y&=\sqrt {x +a}-\sqrt {x +b} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
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