Internal problem ID [4115]
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 21.22, 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-\sin \relax (x )-{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+y(x)=sin(x)+exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+\frac {{\mathrm e}^{-x}}{2}-\frac {x \cos \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.223 (sec). Leaf size: 36
DSolve[y''[x]+y[x]==Sin[x]+Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (2 e^{-x}+\sin (x)-2 x \cos (x)+4 c_1 \cos (x)+4 c_2 \sin (x)\right ) \\ \end{align*}