32.8.16 problem Exercise 21.20, page 231

Internal problem ID [5965]
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
Date solved : Monday, January 27, 2025 at 01:29:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\[ y \left (x \right ) = \frac {\left (36 c_{1} {\mathrm e}^{3 x}+36 \,{\mathrm e}^{2 x} c_{2} +6 x +5\right ) {\mathrm e}^{-x}}{36} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{36} e^{-x} (6 x+5)+c_1 e^x+c_2 e^{2 x} \]