MATH 3705 Midterm: Exam-MATH3705-2003April
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1: lft3e2tg = (d) (a) (b) (c) (d) 2 u(t 3)e 3t sin(2t) (e) none of the above. (s2 + 9)2 = (c) (d) 1 (a) t sin(3t) (b) t sin(3t) (c) t sin(3t) 2 t sin(3t) (d) (e) none of the above: the general solution of 4x2y00 8xy0 + 9y = 0, valid for x 6= 0, is given by (d) (a) c1jxj3=2 + c2jxj3=2 (b) jxj"c1 cos p5. P5(3x) (d) c1jp5(3x) + c2yp5(3x) (e) none of the above: at x = 999, the fourier sine series of f (x) = x on [0; 1] converges to (c) (a) 1 (b) 1 (c) 0 (d) 1. 2 (e) none of the above: the di erential equation 4x2y00 8xy0 + 9 y = 0, when placed in the sturm-liouville form (py0)0 qy + ry = 0, has the weight function r(x) given by (d) (a) 4x4 (e) none of the above: ffe3ix jx 2jg = (a) (a) (b) (c) (d)
