Internal problem ID [5641]
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(h).
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-\left (\tan ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 66
dsolve(diff(y(x),x$2)+4*y(x)=tan(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {-\cos \relax (x ) \left (\cos ^{2}\relax (x )-2 \ln \left (\cos \relax (x )\right )-1\right ) \cos \left (2 x \right )+2 \sin \left (2 x \right ) \left (-\frac {\left (\cos ^{2}\relax (x )\right ) \sin \relax (x )}{2}+x \cos \relax (x )-\frac {\sin \relax (x )}{2}\right )}{2 \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 32
DSolve[y''[x]+4*y[x]==Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_2) \sin (2 x)+\cos (2 x) \left (\log (\cos (x))+\frac {1}{4}+c_1\right )-\frac {3}{4} \\ \end{align*}