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saltydog
#2
Jun12-05, 05:46 AM
Sci Advisor
HW Helper
P: 1,593
Hello Bilgek. Welcome to PF. We have some very bright people in here better than me that I believe can help you. I await their comments. In the interim period may I ask the following:

For the case of f=1, I get:

[tex]2x^{3/2}z^{'}z^{''}=6x^{1/2}(z^{'})^2+4(z^{'})^{5/2}[/tex]

(just use x to make it easy to read for me)
You indicated you solved this analytically. You mind explaining how?

Also, I like the terminology of "singular initial value problem". Do you expect a unique solution? The reason is that I recently worked on:

[tex]ty^{''}+(t-1)y^{'}+y=t^2;\quad y(0)=0,\quad y^{'}(0)=0[/tex]

Yea, I know it's a baby one compared to yours.

Anyway, I obtained a non-unique soltuion at t=0. I would expect the same for your equation. Are you?