Internal problem ID [5647]
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. Challenge excercises. Page 105
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y+3 \cos \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+9*y(x)=-3*cos(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}-\frac {3 \cos \left (2 x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 28
DSolve[y''[x]+9*y[x]==-3*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3}{5} \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \\ \end{align*}