32.8.22 problem Exercise 21.29, page 231

Internal problem ID [5971]
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
Date solved : Monday, January 27, 2025 at 01:29:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=5 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (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)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{6} \left (e^{-x}+2 e^{2 x}-9 \sin (x)+3 \cos (x)\right ) \]