20.12.4 problem Problem 19

Internal problem ID [3798]
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 19
Date solved : Monday, January 27, 2025 at 08:02:27 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=4*exp(-2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-3 x}+4 \,{\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==4*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (4 e^x+c_2 x+c_1\right ) \]