78.5.24 problem 4 (m)

Internal problem ID [18167]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (m)
Date solved : Tuesday, January 28, 2025 at 11:35:54 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)+y(x)/x=sin(x),y(x), singsol=all)
 

\[ y = \frac {\sin \left (x \right )-x \cos \left (x \right )+c_1}{x} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 19

DSolve[D[y[x],x]+y[x]/x==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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