73.15.26 problem 22.9 (d)

Internal problem ID [15457]
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)
Date solved : Tuesday, January 28, 2025 at 07:56:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=3 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+9*y(x)=3*sin(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (-x +2 c_{1} \right ) \cos \left (3 x \right )}{2}+\sin \left (3 x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 62

DSolve[D[y[x],{x,2}]+9*y[x]==3*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (3 x) \int _1^x\frac {1}{2} \sin (6 K[2])dK[2]+\cos (3 x) \int _1^x-\sin ^2(3 K[1])dK[1]+c_1 \cos (3 x)+c_2 \sin (3 x) \]