50.14.18 problem 3(b)

Internal problem ID [8056]
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)
Date solved : Monday, January 27, 2025 at 03:40:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{2 x} c_{1} +\frac {{\mathrm e}^{-x}}{6}+{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{-x}}{6}+c_1 e^x+c_2 e^{2 x} \]