Internal problem ID [5567]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-{\mathrm e}^{-x} \sec \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 52
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=exp(-x)*sec(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{-x} \cos \left (2 x \right ) c_{1}+\frac {\left (2 x \sin \left (2 x \right )-\cos \left (2 x \right ) \ln \left (\frac {1}{\cos \left (2 x \right )}\right )\right ) {\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 42
DSolve[y''[x]+2*y'[x]+5*y[x]==Exp[-x]*Sec[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x} (2 (x+2 c_1) \sin (2 x)+\cos (2 x) (\log (\cos (2 x))+4 c_2)) \\ \end{align*}