32.9.1 problem Exercise 22.1, page 240

Internal problem ID [5975]
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
Date solved : Monday, January 27, 2025 at 01:29:42 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+y[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+c_2) \sin (x)+\cos (x) (\log (\cos (x))+c_1) \]