8.22 problem Exercise 21.29, page 231

Internal problem ID [4119]

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 21.29, 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 }-y^{\prime }-2 y-5 \sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 25

dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=5*sin(x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {{\mathrm e}^{2 x}}{3}+\frac {{\mathrm e}^{-x}}{6}+\frac {\cos \relax (x )}{2}-\frac {3 \sin \relax (x )}{2} \]

Solution by Mathematica

Time used: 0.01 (sec). Leaf size: 30

DSolve[{y''[x]-y'[x]-2*y[x]==5*Sin[x],{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (e^{-x}+2 e^{2 x}-9 \sin (x)+3 \cos (x)\right ) \\ \end{align*}