Internal problem ID [4105]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-8 y-9 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \relax (x ) = {\mathrm e}^{4 x} c_{2}+{\mathrm e}^{-2 x} c_{1}-x \,{\mathrm e}^{x}-2 \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 35
DSolve[y''[x]-2*y'[x]-8*y[x]==9*x*Exp[x]+10*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (-e^{3 x} x-2 e^x+c_2 e^{6 x}+c_1\right ) \\ \end{align*}