# how to solve IVP using separable variable

the question is:

x dy/dx= 2y ; y(0)=0

because when i solve this problem the integration constant 'c' gets zero... and i have to find its value in order to calculate a solution to given IVP

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@ Sadia: Are you sure this question is stated correctly. Because the ODE yields a solution of zero. –  night owl Jul 4 '11 at 12:14

Solving this problem, I get $$y = ax^2$$ with $a$ a constant. Could you use this constant to find a solution for your IVP ?
I don't think this differential equation has a unique solution, if you check http://planetmath.org/encyclopedia/PicardsTheorem2.html you see that $$f(x,y) = \frac{2y}{x}$$ is not continuous in $(0,0)$, so Picard's Theorem doesn't hold.