Internal problem ID [5636]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(c).
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-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1}-\frac {3 \cos \relax (x )}{10}-\frac {\sin \relax (x )}{10} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 34
DSolve[y''[x]-y'[x]-2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sin (x)}{10}-\frac {3 \cos (x)}{10}+c_1 e^{-x}+c_2 e^{2 x} \\ \end{align*}