MATH 257 Study Guide - Midterm Guide: Regular Singular Point, Tonne, Heat Equation
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Do not open this test until instructed to do so. It is a closed book exam; no textbooks, calculators, laptops, formula sheets or other aids are allowed. Turn o any cell phones, pagers, etc. that could make noise during the exam. You must remain in this room until you have nished the exam. Please explain your work, and circle your nal solutions. Consider the ordinary di erential equation x2 d2y dx2 +(cid:0)2x x2(cid:1) dy dx. Consider the heat equation with a source ut = uxx + sin x, 2 n ( 1)n n = 1 n 2 (c) [8] by writing u(x, t) = u (x)+v(x, t) and separating variables, determine the solution for u(x, t). Problem 3 (20 points) (a) [10] waves on a string that is xed at ends x = 0 and x = 8 satisfy utt = c2uxx,
