Internal problem ID [4131]
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.
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-{\mathrm e}^{-x} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=exp(-x)*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+\frac {x^{2} \left (2 \ln \relax (x )-3\right ) {\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 36
DSolve[y''[x]+2*y'[x]+y[x]==Exp[-x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}