32.9.4 problem Exercise 22.4, page 240

Internal problem ID [5978]
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 22.4, page 240
Date solved : Monday, January 27, 2025 at 01:29:52 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-y(x)=sin(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{-x} c_{1} +\frac {\cos \left (x \right )^{2}}{5}-\frac {3}{5} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{10} (\cos (2 x)-5)+c_1 e^x+c_2 e^{-x} \]