Particular Integral calculation

[esmeco]

Homework Statement

I was wondering,how do you calculate the particular integral for a differential equation that satisfies a given equation?

Homework Equations

For example an equation like this: (dy/dx)*squareroot of x - squareroot of y= x*square root of y where the values of x and y are: (x,y)=(9.4)

The Attempt at a Solution

I tried to solve this equation using the separated variables theorem but I dn't know what to do next!

 

[Hurkyl]

Well, we can't tell you what to do next if you don't tell us where you got stuck!

 

[esmeco]

This's my attempt to the solution(see attachment)