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**ceramica** Does anyone can help me to solve this second order non linear ODE:

y'' + (2/x)(y') - (1/2y)(y')(y') = K,

y' = dy/dx

y'' = dy'/dx

y = y(x)

I've already guess y=Ax^2 satisfy this equation, but I want to solve it analitically..

I have transform the equation above with x=-(1/u) and f = ln H, that lead to a new equation:

f'' + (1/2)(f')(f') = -(K/u^4)exp{-f}

f = f(u)

f' = df/du

f'' = df'/du

but still cannot find the solution analitically.

Is y'' + (2/x)(y') - (1/2y)(y')(y') = K cannot be solved analitically?

It seem strange to me that an an ODE with a simple subtitution solution y=Ax^2 don't have any analytical solution..

Please help!

Thanks before..