MATH300 Midterm: MATH 300 UofA Midterm A Solutions

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turquoisegnu128

31 Jan 2019

School

University of Alberta

Department

Mathematics

Course

MATH300

Professor

All

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Document Summary

Find the values of 2 for which the boundary value problem. 2 d2u dx2 + 2u = 0, u(0) = 0. 0 u(t) dt = 0 has non-trivial solutions. Solution: we consider two cases: case (i): = 0. In this case, the general solution to so that u(x) = ax. 2 d2u dx2 = 0 is given by u(x) = ax + b, and u(0) = 0 implies that b = 0, u(t) dt = 0 implies that. 2 (cid:12)(cid:12)(cid:12)(cid:12) which implies that a = 0, and the boundary value problem has only the trivial solution in this case. case (ii): 6= 0. B sin t dt = and so either b = 0 or cos . Therefore, a nontrivial solution exists if and only if we have cos an integer. The values of 2 for which the boundary value problem has non-trivial solutions are.

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MATH300 Midterm: MATH 300 UofA Midterm A Solutions

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