73.15.16 problem 22.7 (a)

Internal problem ID [15447]
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 : 22.7 (a)
Date solved : Tuesday, January 28, 2025 at 07:56:07 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 33

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

\[ y(x)\to 4 \sin (2 x)+5 x \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]