Internal problem ID [5643]
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: 4(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y+8 \sin \left (3 x \right )=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= \sin \left (3 x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+y(x)=-8*sin(3*x),sin(3*x)],y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}+\sin \left (3 x \right )+\frac {3 \sin \relax (x )}{2} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==-8*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (3 x)+c_1 \cos (x)+(2+c_2) \sin (x) \\ \end{align*}