Internal problem ID [11670]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(cos(y(x))*diff(y(x),x)+1/x*sin(y(x))=1,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (\frac {-x^{2}+2 c_{1}}{2 x}\right ) \]
✓ Solution by Mathematica
Time used: 8.67 (sec). Leaf size: 18
DSolve[Cos[y[x]]*y'[x]+1/x*Sin[y[x]]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (\frac {x}{2}+\frac {c_1}{x}\right ) \]