11.11 problem 2(e)

Internal problem ID [5574]

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

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

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

Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

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

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

Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 49

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

\begin{align*} y(x)\to c_2 \sin (x)+\cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right ) \\ \end{align*}