Internal problem ID [228]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 10.
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-2 \cos \left (3 x \right )-3 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)+9*y(x)=2*cos(3*x)+3*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}+\frac {\left (-9 x +2\right ) \cos \left (3 x \right )}{18}+\frac {\sin \left (3 x \right ) x}{3} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 39
DSolve[y''[x]+9*y[x]==2*Cos[3*x]+3*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {x}{2}+\frac {1}{9}+c_1\right ) \cos (3 x)+\frac {1}{12} (4 x+1+12 c_2) \sin (3 x) \\ \end{align*}