Internal problem ID [4123]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.1, page 240.
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: 0.003 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\sin \relax (x ) x -\ln \left (\frac {1}{\cos \relax (x )}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.009 (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*}