Internal problem ID [2323]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page
575
Problem number: Problem 28.
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-2 x \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*x*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} c_{2}+x \,{\mathrm e}^{-x} c_{1}+\frac {{\mathrm e}^{-x} x^{3}}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[y''[x]+2*y'[x]+y[x]==2*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x} \left (x^3+3 c_2 x+3 c_1\right ) \\ \end{align*}