Internal problem ID [6388]
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]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \left ({\mathrm e}^{x} c_{1} +\frac {{\mathrm e}^{-2 x}}{6}+c_{2} \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 29
DSolve[y''[x]-3*y'[x]+2*y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x}}{6}+c_1 e^x+c_2 e^{2 x} \]