12.10 problem Ex 11

Internal problem ID [10166]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number: Ex 11.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve((x*sin(y(x)/x)-y(x)*cos(y(x)/x))+x*cos(y(x)/x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = x \arcsin \left (\frac {1}{x c_{1}}\right ) \]

Solution by Mathematica

Time used: 13.014 (sec). Leaf size: 21

DSolve[(x*Sin[y[x]/x]-y[x]*Cos[y[x]/x])+x*Cos[y[x]/x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \text {ArcSin}\left (\frac {e^{c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}