MATH 257 Study Guide - Midterm Guide: Boundary Value Problem, Briey, Dependent Source
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Final examination - 12 noon december 17, 2015. 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. 6x2y00 + 5xy0 (1 + x)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) [14 marks] (b) brie y describe how you would use the method of nite differences to obtain an approximate solution to this boundary value problem that is accurate to o( x2, t) terms. Use the notation uk n " u(xn, tk) to represent the nodal values on the nite difference mesh.
