Internal problem ID [4122]
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]]
\[ \boxed {y^{\prime \prime }+y-\sec \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+x \sin \left (x \right )-\ln \left (\sec \left (x \right )\right ) \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.008 (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*}