11.12 problem 2(f)

Internal problem ID [5575]

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: 2(f).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sec \relax (x ) \tan \relax (x )=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+y(x)=sec(x)*tan(x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 25

DSolve[y''[x]+y[x]==Sec[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to (x+c_1) \cos (x)+\sin (x) (-\log (\cos (x))-1+c_2) \\ \end{align*}