I know the solution to the Boundary layer problem is something like this:


I have the Inner expansion as:

$$Y_{0}\left( x\right) \sim 1+c\int _{0}^{x}e^{-9x^{\frac {4} {3}}}ds,$$

and the outer expansion as as:

$$y_{0}\left( x\right) \sim e^{\frac {1-x^{\frac {2} {3}}} {8}}.$$

The problem i have is finding $c$. I know you do asymptotic matching by:


How to i find the constant $c$ which could be something like this:

$$C=\dfrac {4\sqrt {3}\left( e^{1 / 8}-1\right) } {\Gamma \left( \dfrac {3} {4}\right) }$$

(Teacher was going to fast to explain, i might have copied it down wrong). And then to put into form of a "uniform solution".


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