50.15.2 problem 4

Internal problem ID [8068]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Challenge excercises. Page 105
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:41:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 28

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

\[ y(x)\to -\frac {3}{5} \cos (2 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]