Internal problem ID [2317]
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 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+6 y^{\prime }+9 y-4 \,{\mathrm e}^{-3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=4*exp(-3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-3 x}+{\mathrm e}^{-3 x} x c_{1}+2 \,{\mathrm e}^{-3 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 22
DSolve[y''[x]+6*y'[x]+9*y[x]==4*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} (x (2 x+c_2)+c_1) \\ \end{align*}