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^{2}y/dx

^{2}= C/y, where C is some constant, such equation take place when deriving equation of motion in gravitationnal field, I'm more interested in how to solve it, yet I only managed to express it as power series using taylor's theorem at x = 0, just pick y(0) = c1, y'(0) = c2, so y''= C/c1, y'''(x) = C*c2/c1

^{2}and so on, until y ≈ c1 + c2*x + C/2c1 * x

^{2}+ C*c2/6c1

^{2}*x

^{3}+ ......., Is there's any special function that solves the equation or any other approximisation ?, I want to hear some thoughts !,