Internal problem ID [4113]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.20, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-x \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=x*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1} {\mathrm e}^{x}+\frac {5 \,{\mathrm e}^{-2 x}}{36}+\frac {{\mathrm e}^{-2 x} x}{6}+c_{2}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 34
DSolve[y''[x]-3*y'[x]+2*y[x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} e^{-x} (6 x+5)+c_1 e^x+c_2 e^{2 x} \\ \end{align*}