73.15.71 problem 22.14 (b)

Internal problem ID [15502]
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 : 22.14 (b)
Date solved : Tuesday, January 28, 2025 at 07:59:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 42

dsolve(diff(y(x),x$2)+9*y(x)=25*x*cos(2*x)+3*sin(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (-x +2 c_{1} \right ) \cos \left (3 x \right )}{2}+\frac {\left (1+12 c_{2} \right ) \sin \left (3 x \right )}{12}+5 x \cos \left (2 x \right )+4 \sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.638 (sec). Leaf size: 96

DSolve[D[y[x],{x,2}]+9*y[x]==25*x*Cos[2*x]+3*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (3 x) \int _1^x-\frac {1}{3} \sin (3 K[1]) (25 \cos (2 K[1]) K[1]+3 \sin (3 K[1]))dK[1]+\sin (3 x) \int _1^x\frac {1}{3} \cos (3 K[2]) (25 \cos (2 K[2]) K[2]+3 \sin (3 K[2]))dK[2]+c_1 \cos (3 x)+c_2 \sin (3 x) \]