Internal problem ID [5564]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\tan \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+4*y(x)=tan(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}-\frac {\cos \left (2 x \right ) \ln \left (\frac {1+\sin \left (2 x \right )}{\cos \left (2 x \right )}\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 37
DSolve[y''[x]+4*y[x]==Tan[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left ((-1+4 c_2) \sin (2 x)-\cos (2 x) \left (\tanh ^{-1}(\sin (2 x))-4 c_1\right )\right ) \\ \end{align*}