MATH 257 Study Guide - Midterm Guide: Heat Equation, Thermal Conduction, Boundary Value Problem
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Page 2 of 17 pages: consider the differential equation (a) classify the points 0 x < as ordinary points, regular singular points, or irregular singular points. 2x2y00 xy0 + (1 + x2)y = 0 (1) (b) Find two values of r such that there are solutions of the form y(x) = P n=0 anxn+r. (c) use the series expansion in (b) to determine two independent solutions of (1). You only need to calculate the rst three non-zero terms in each case. Page 3 of 17 pages (question 1 continued) Page 4 of 17 pages (question 1 continued) Page 5 of 17 pages: consider a conducting metal bar of length /2 whose initial temperature is u(x, 0) = x and which loses heat to its surroundings. Assume that the left end of the bar is maintained at a zero temperature while the right end is insulated.
