Internal problem ID [1156]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 2.
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-\sin \left (2 x \right ) \left (\sec ^{2}\left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)+4*y(x)=sin(2*x)*sec(2*x)^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {\left (-\ln \left (\cos \left (2 x \right )\right )-1\right ) \sin \left (2 x \right )}{4}+\frac {x \cos \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Sin[2*x]*Sec[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-x+c_1) \cos (2 x)+\sin (x) \cos (x) (2 \log (\cos (x))-1+2 c_2) \\ \end{align*}