78.13.2 problem 1 (b)

Internal problem ID [18324]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (b)
Date solved : Tuesday, January 28, 2025 at 11:46:21 AM
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: 0.003 (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: 0.016 (sec). Leaf size: 22

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

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