Internal problem ID [6391]
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]]
\[ \boxed {y^{\prime \prime }+9 y=\sec \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 81
dsolve(diff(y(x),x$2)+9*y(x)=sec(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2}{3}+\frac {\left (-4 \cos \left (x \right )^{3}+3 \cos \left (x \right )\right ) \sqrt {2}\, \operatorname {arctanh}\left (\cos \left (x \right ) \sqrt {2}\right )}{6}+\frac {\sin \left (x \right ) \left (1-4 \cos \left (x \right )^{2}\right ) \sqrt {2}\, \operatorname {arctanh}\left (\sin \left (x \right ) \sqrt {2}\right )}{6}+4 c_{1} \cos \left (x \right )^{3}+\frac {4 \left (3 \sin \left (x \right ) c_{2} +1\right ) \cos \left (x \right )^{2}}{3}-3 \cos \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.25 (sec). Leaf size: 102
DSolve[y''[x]+9*y[x]==Sec[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (-\sqrt {2} \sin (3 x) \text {arctanh}\left (\sqrt {2} \sin (x)\right )-\sqrt {2} \cos (3 x) \text {arctanh}\left (\sqrt {2}-\tan \left (\frac {x}{2}\right )\right )-\sqrt {2} \cos (3 x) \text {arctanh}\left (\tan \left (\frac {x}{2}\right )+\sqrt {2}\right )+4 \cos (2 x)+6 c_1 \cos (3 x)+6 c_2 \sin (3 x)\right ) \]