64.5.33 problem 37 (a)

Internal problem ID [13346]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 37 (a)
Date solved : Tuesday, January 28, 2025 at 05:31:18 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(cos(y(x))*diff(y(x),x)+1/x*sin(y(x))=1,y(x), singsol=all)
 

\[ y = -\arcsin \left (\frac {-x^{2}+2 c_{1}}{2 x}\right ) \]

✓ Solution by Mathematica

Time used: 8.255 (sec). Leaf size: 18

DSolve[Cos[y[x]]*D[y[x],x]+1/x*Sin[y[x]]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {x}{2}+\frac {c_1}{x}\right ) \]