Internal problem ID [2832]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=2 x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left (c_{2} +c_{1} x +\frac {1}{3} x^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 27
DSolve[y''[x]+2*y'[x]+y[x]==2*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-x} \left (x^3+3 c_2 x+3 c_1\right ) \]