Internal problem ID [247]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 52.
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: 0.0 (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: 0.018 (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*}