Internal problem ID [4685]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page
109
Problem number: Problem 12.10.
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 )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+x \sin \relax (x )-\ln \left (\frac {1}{\cos \relax (x )}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_2) \sin (x)+\cos (x) (\log (\cos (x))+c_1) \\ \end{align*}