| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 14.2 (a) |
\begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
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| Problem 14.2 (b) |
\begin{align*}
\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1}&=0 \\
\end{align*} |
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| Problem 14.2 (c) |
\begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
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| Problem 14.3 (a) |
\begin{align*}
y \left (2 y^{2} x^{2}+1\right ) y^{\prime }+x \left (1+y^{4}\right )&=0 \\
\end{align*} |
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| Problem 14.3 (b) |
\begin{align*}
2 y^{\prime } x +3 x +y&=0 \\
\end{align*} |
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| Problem 14.3 (c) |
\begin{align*}
\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
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| Problem 14.5 (a) |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
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| Problem 14.5 (b) |
\begin{align*}
y^{\prime }-\cot \left (x \right ) y+\frac {1}{\sin \left (x \right )}&=0 \\
\end{align*} |
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| Problem 14.5 (c) |
\begin{align*}
\left (y^{3}+x \right ) y^{\prime }&=y \\
\end{align*} |
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| Problem 14.6 |
\begin{align*}
y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\
\end{align*} |
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| Problem 14.11 |
\begin{align*}
\left (-x +y\right ) y^{\prime }+2 x +3 y&=0 \\
\end{align*} |
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| Problem 14.14 |
\begin{align*}
y^{\prime }&=\frac {1}{x +2 y+1} \\
\end{align*} |
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| Problem 14.15 |
\begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
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| Problem 14.16 |
\begin{align*}
y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \\
\end{align*} |
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| Problem 14.17 |
\begin{align*}
x \left (1-2 x^{2} y\right ) y^{\prime }+y&=3 y^{2} x^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
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| Problem 14.23 (a) |
\begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
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| Problem 14.23 (b) |
\begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
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| Problem 14.24 (a) | \begin{align*}
y^{\prime }-\frac {y}{x}&=1 \\
y \left (1\right ) &= -1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ |
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| Problem 14.24 (b) |
\begin{align*}
y^{\prime }-\tan \left (x \right ) y&=1 \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
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| Problem 14.24 (c) |
\begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| Problem 14.24 (d) |
\begin{align*}
y^{\prime }-\frac {y^{2}}{x^{2}}&={\frac {1}{4}} \\
\end{align*} |
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| Problem 14.26 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
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| Problem 14.28 |
\begin{align*}
\left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\
\end{align*} |
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| Problem 14.29 |
\begin{align*}
y^{\prime } x +y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
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| Problem 14.30 (a) |
\begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| Problem 14.30 (b) |
\begin{align*}
\left (2 \sin \left (y\right )-x \right ) y^{\prime }&=\tan \left (y\right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
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| Problem 14.31 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 15.1 |
\begin{align*}
x^{\prime \prime }+\omega _{0}^{2} x&=a \cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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| Problem 15.2(a) |
\begin{align*}
f^{\prime \prime }+2 f^{\prime }+5 f&=0 \\
f \left (0\right ) &= 1 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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| Problem 15.2(b) |
\begin{align*}
f^{\prime \prime }+2 f^{\prime }+5 f&={\mathrm e}^{-t} \cos \left (3 t \right ) \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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| Problem 15.4 |
\begin{align*}
f^{\prime \prime }+6 f^{\prime }+9 f&={\mathrm e}^{-t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= \lambda \\
\end{align*} |
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| Problem 15.5(a) |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
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| Problem 15.5(b) |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
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| Problem 15.7 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
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| Problem 15.9(a) |
\begin{align*}
y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \\
\end{align*} |
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| Problem 15.9(b) |
\begin{align*}
-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}&=2 a^{2} \\
\end{align*} |
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| Problem 15.21 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
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| Problem 15.22 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y&=x^{2} \\
\end{align*} |
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| Problem 15.23 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}&=0 \\
\end{align*} |
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| Problem 15.24(a) |
\begin{align*}
y^{\prime \prime }-y&=x^{n} \\
\end{align*} |
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| Problem 15.24(b) |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
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| Problem 15.33 |
\begin{align*}
2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \\
\end{align*} |
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| Problem 15.34 |
\begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \\
\end{align*} |
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| Problem 15.35 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&={\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \\
\end{align*} |
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| ID | problem | ODE | Solved? | Maple | Mma | Sympy |
| Problem 16.1 |
\begin{align*}
\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.2 |
\begin{align*}
4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.3 |
\begin{align*}
z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.4 |
\begin{align*}
f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.6 |
\begin{align*}
z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (z +1\right ) y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.8 |
\begin{align*}
z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.9 |
\begin{align*}
y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.10 |
\begin{align*}
z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.11 |
\begin{align*}
z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.12 (a) |
\begin{align*}
\left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.12 (b) |
\begin{align*}
\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.13 |
\begin{align*}
y^{\prime \prime }+\frac {y}{z^{3}}&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.14 |
\begin{align*}
z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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| Problem 16.15 |
\begin{align*}
\left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \\
\end{align*} Series expansion around \(z=0\). |
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