32.8.8 problem Exercise 21.10, page 231

Internal problem ID [5957]
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 21.10, page 231
Date solved : Monday, January 27, 2025 at 01:28:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-2*diff(y(x),x)-8*y(x)=9*x*exp(x)+10*exp(-x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 35

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-8*y[x]==9*x*Exp[x]+10*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (-e^{3 x} x-2 e^x+c_2 e^{6 x}+c_1\right ) \]