Internal problem ID [5209]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(b).
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-\sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+9*y(x)=sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}-\frac {\cos \left (3 x \right ) x}{6} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {x}{6}+c_1\right ) \cos (3 x)+\frac {1}{36} (1+36 c_2) \sin (3 x) \\ \end{align*}