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I need to solve the following second order nonlinear differential equation:

z''(b) * [6(1 - f)z(b) + (1+f)b z'(b)] = (15 - 9 f)[z'(b)]^2 + [2(1 - f) z(b) z'(b)] / b + [4 f z'(b)^(5/2)] / b^(1/2)

where f is a constant between [0,1].

initial conditions are z(0)=0 and z'(0)=0

I couldn't solve it analytically (except for f = 1 case). I tried numerical solution but my initial conditions have singularity.

In case, here is the more detailed Pdf file for the equation:

http://www.people.virginia.edu/~bk5w/home_files/trouble.pdf [Broken]

I don't know whether this is a singularity of first kind of the second.

I wonder whether you guys can help me to solve this problem.

Thanks

z''(b) * [6(1 - f)z(b) + (1+f)b z'(b)] = (15 - 9 f)[z'(b)]^2 + [2(1 - f) z(b) z'(b)] / b + [4 f z'(b)^(5/2)] / b^(1/2)

where f is a constant between [0,1].

initial conditions are z(0)=0 and z'(0)=0

I couldn't solve it analytically (except for f = 1 case). I tried numerical solution but my initial conditions have singularity.

In case, here is the more detailed Pdf file for the equation:

http://www.people.virginia.edu/~bk5w/home_files/trouble.pdf [Broken]

I don't know whether this is a singularity of first kind of the second.

I wonder whether you guys can help me to solve this problem.

Thanks

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