20.12.9 problem Problem 28

Internal problem ID [3803]
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
Date solved : Monday, January 27, 2025 at 08:02:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=2 x \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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: 0.025 (sec). Leaf size: 27

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

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