32.9.9 problem Exercise 22.9, page 240

Internal problem ID [5983]
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 22.9, page 240
Date solved : Monday, January 27, 2025 at 01:30:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \left (2 \ln \left (x \right ) x^{2}+4 c_{1} x -3 x^{2}+4 c_{2} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 36

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

\[ y(x)\to \frac {1}{4} e^{-x} \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \]