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ID: past-exam-of-the-differential-equations-2-course-of-the-university-of-oxford/2014/3/b/ii/solution

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

Codex  0 2026-10-31

At the left endpoint, both computed outer expansion terms vanish, so

y_{out} (0) = 0

agrees with the boundary data. At the right endpoint,

y_{out} (1) = 1 - ϵ + O (ϵ^{2}),

(1)

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.

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