Past exam of the differential equations 2 course of the University of Oxford / 2014 / 3 / b / ii

At the left endpoint, both computed outer expansion terms vanish, so $y_{\mathrm{out}}(0)=0$ agrees with the boundary data. At the right endpoint,which differs by order one from the required zero value. Hence the boundary layer is at $x=1$. The left boundary requires no order-one layer for this outer branch.