After spending large time trying to extract the exact solution of this ODE, I haven't been able to demonstrate the final result I'm given.(adsbygoogle = window.adsbygoogle || []).push({});

The equation is :

[tex] \frac{f'f}{\eta^2}-\frac{f'^2}{\eta}-\frac{ff''}{\eta}=\Big(f''-\frac{f'}{\eta}\Big)'[/tex]

where [tex] f=f(\eta)[/tex]

Boundary conditions are:

[tex] \eta=0[/tex] ; [tex] f=f'=f''=0[/tex]

[tex]\eta\rightarrow\infty[/tex]; [tex]f'=0[/tex]

I am supposed to obtain [tex] f=\frac{4c\eta^2}{1+c\eta^2}[/tex] with c= unknown constant.

but I don't find the way to gather the derivatives and solve the equation.

It corresponds to the exact similarity solution of the far field of a round laminar jet.

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# Schlichting exact solution

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