I'm having trouble rewriting differential equations in the form F(v). That is, changing a function to make it's variables have the form "y/x" so I can perform the substitution v=y/x. Here's a sample problem:

Solve the differential equation:

yy'= sqrt(x^2+y^2)-x

Is there a general way to go about transforming this into the form f(v)?

Any help would be much appreciated.

Thank!