Consider $$ \epsilon y'' + x^{\alpha} y' + y = 0 , \; \; \; \; \epsilon \to 0^+ $$
with $y(0)=y(1)=1$. For what value of $\alpha$ there is boundary layer at $x=0$? What is the thickness of the boundary layer?
Try:
I know there is a boundary layer near $x = 0$ if $x^{\alpha} >0 $ which means that we want $\alpha = 2k $ for $k \in \mathbb{Z}$. Im stuck on trying to find the thickness of the BL
As $x^α>0$ for any $x>0$, there is no special demand on $α$.
You need to balance for $Y(X)=y(\delta X)$ $$ ϵY''(X)+δ^{α+1}X^αY'(X)+δ^2Y(X)=0 $$ so that you have to consider the cases $α+1<2$, $α+1>2$ and $α+1=2$.