Originally Posted by
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..