Find the general solution of the following differential equation

[Illusionist]

Homework Statement

Find the general solution of the following differential equation:
x.(dy/dx) = y + sqrt.[(x^2) - (y^2)]

Homework Equations

I'm working through my excerise book and have been able to get through quite a few differential equations with success, but this one really does stump me. I think it's the sqrt.[(x^2) - (y^2)] that gets me confused.

The Attempt at a Solution

My first step was to divide both sides by x to get dy/dx alone, hence:
(dy/dx) = y + [ sqrt.[(x^2) - (y^2)] / x ]

This is where I begin to get lost. My natural instinct is to try and separate the x and y's but I can't seem to and the next step for is a mystery to me. I'm having a lot of troule identifying what sort of approach to use.

Any help would be very appreciated, thank you in advance.

 

[siddharth]

My first step was to divide both sides by x to get dy/dx alone, hence:
(dy/dx) = y + [ sqrt.[(x^2) - (y^2)] / x ]

Not quite. You get,

(dy/dx) = y/x + sqrt.[1 - (y/x)^2]

Try y=ux