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Find all the solutions of the equation:

##\dfrac{\sin(y)}{x}dx+(\dfrac{y}{x}\cos(y)-\dfrac{\sin(y)}{y})dy=0## knowing that the equation admits an integrating factor ##u## of the form ##u(x,y)=h(\dfrac{x}{y})##

The attempt at a solution.

If I call ##M(x,y)=\dfrac{\sin(y)}{x}## and ##N(x,y)=\dfrac{y}{x}\cos(y)-\dfrac{\sin(y)}{y}## then, in order to be an exact differential equation, ##M## and ##N## must satisfy ##M_y=N_x##, but ##M_y=\dfrac{\cos(y)}{x}≠-\dfrac{y\cos(y)}{x^2}=N_x##, so this is not an exact differential equation.

As the exercise suggests, I've tried to propose an integrating factor ##u## of the form ##u(x,y)=h(\dfrac{x}{y})##, but, since up to know I've only solved equations where the integrating factor depended just on one of the variables, I got stuck in the middle of the problem.

So, ##u## must satisfy:

##(uM)dx+(uN)dy=0##

Then, ##(uM)_y=(uN)_x \iff u_yM+uM_y=u_xN+uN_x \iff xh_yM+hM_y=\dfrac{1}{y}h_xN+hN_x##.

Calculating all these partial derivatives gives:

##xh_y\dfrac{\sin(y)}{x}+h\dfrac{\cos(y)}{x}=\dfrac{1}{y}h_x(\dfrac{ycos(y)}{x}-\dfrac{\sin(y)}{y})+h(-\dfrac{ycos(y)}{x^2})##

At this point I got stuck and I don't know what and how to integrate in order to find ##u(x,y)##