Internal problem ID [4134]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-\frac {{\mathrm e}^{-x}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=exp(-x)/x,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+x \left (\ln \relax (x )-1\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 24
DSolve[y''[x]+2*y'[x]+y[x]==Exp[-x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (x \log (x)+(-1+c_2) x+c_1) \\ \end{align*}