50.14.26 problem 4(b)

Internal problem ID [8064]
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. Drill excercises. Page 105
Problem number : 4(b)
Date solved : Monday, January 27, 2025 at 03:41:16 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=-8 \sin \left (3 x \right ) \end{align*}

Using reduction of order method given that one solution is

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)+y(x)=-8*sin(3*x),sin(3*x)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[y[x],{x,2}]+y[x]==-8*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

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