14.18 problem 3(b)

Internal problem ID [5635]

Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(b).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-{\mathrm e}^{-x}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(-x),y(x), singsol=all)
 

\[ y \relax (x ) = \left (c_{1} {\mathrm e}^{x}+\frac {{\mathrm e}^{-2 x}}{6}+c_{2}\right ) {\mathrm e}^{x} \]

Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 29

DSolve[y''[x]-3*y'[x]+2*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{-x}}{6}+c_1 e^x+c_2 e^{2 x} \\ \end{align*}