Internal problem ID [5638]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-\sec \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)+9*y(x)=sec(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {\left (-\sqrt {2}\, \arctanh \left (\sqrt {2}\, \cos \relax (x )\right )+4 \cos \relax (x )\right ) \cos \left (3 x \right )}{6}-\frac {\sin \left (3 x \right ) \left (\sqrt {2}\, \arctanh \left (\sqrt {2}\, \sin \relax (x )\right )-4 \sin \relax (x )\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.517 (sec). Leaf size: 136
DSolve[y''[x]+9*y[x]==Sec[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} \left (16 \cos (2 x)-4 \sin (3 x) \left (\sqrt {2} \tanh ^{-1}\left (\sqrt {2} \sin (x)\right )-6 c_2\right )+\cos (3 x) \left (-4 \sqrt {2} \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )+\sqrt {2}\right )+\sqrt {2} \log \left (-\sqrt {2} \sin (x)-\sqrt {2} \cos (x)+2\right )-\sqrt {2} \log \left (-\sqrt {2} \sin (x)+\sqrt {2} \cos (x)+2\right )+\frac {i \pi }{\sqrt {2}}+24 c_1\right )\right ) \\ \end{align*}