32.9.15 problem Exercise 22.15, page 240

Internal problem ID [5989]
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 22.15, page 240
Date solved : Monday, January 27, 2025 at 01:30:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\cos \left ({\mathrm e}^{-x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=cos(exp(-x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Cos[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (-e^x \cos \left (e^{-x}\right )+c_2 e^x+c_1\right ) \]