50.10.2 problem 1(b)

Internal problem ID [7971]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:34:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=3 \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)+4*y(x)=3*sin(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+4*y[x]==3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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