32.9.3 problem Exercise 22.3, page 240

Internal problem ID [5977]
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 22.3, page 240
Date solved : Monday, January 27, 2025 at 01:29:48 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 28

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

\[ y(x)\to 2 \sin (x) \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )+c_1 \cos (x)+c_2 \sin (x)-1 \]