Internal problem ID [13721]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.9 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=3 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+9*y(x)=3*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} -x \right ) \cos \left (3 x \right )}{2}+c_{2} \sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==3*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{2}+c_1\right ) \cos (3 x)+\frac {1}{12} (1+12 c_2) \sin (3 x) \]