50.11.4 problem 1(d)

Internal problem ID [7988]
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)
Date solved : Monday, January 27, 2025 at 03:35:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&={\mathrm e}^{-x} \sec \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=exp(-x)*sec(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-\frac {\cos \left (2 x \right ) \ln \left (\sec \left (2 x \right )\right )}{2}+2 \cos \left (2 x \right ) c_{1} +\sin \left (2 x \right ) \left (x +2 c_{2} \right )\right ) {\mathrm e}^{-x}}{2} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==Exp[-x]*Sec[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-x} (2 (x+2 c_1) \sin (2 x)+\cos (2 x) (\log (\cos (2 x))+4 c_2)) \]