32.9.12 problem Exercise 22.12, page 240

Internal problem ID [5986]
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 22.12, page 240
Date solved : Monday, January 27, 2025 at 01:30:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\frac {{\mathrm e}^{-x}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 24

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

\[ y(x)\to e^{-x} (x \log (x)+(-1+c_2) x+c_1) \]