exam2 - = cos 4x , y ' = y' = . 3] The function f x is...

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Engineering Analysis Exam 2 1] (a) By assuming solutions in the form of power series about x = 0, find two independent solutions for the differential equation 1 x 2 d 2 y dx 2 2x dy dx 2y = 0 . (b) Determine the convergence radius of the two power-series solutions. (c) This equation is a special case of what particular second-order ODE, discussed in class? 2] (a) Consider the proper Sturm-Liouville problem d 2 y dx 2  y = 0, y ' 0 = y ' = 0 . What are the characteristic numbers and characteristic functions? (b) Use your results from (a) to solve the problem d 2 y dx 2 3y
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Unformatted text preview: = cos 4x , y ' = y' = . 3] The function f x is periodic with period 2 . Over [ , ] , it is given by f x = 1 if x is in [/ 2, / 2 ] f x = otherwise. Find a Fourier series representation of f x , valid over the entire real line. Possibly useful formulas: Quadratic formula: x = b b 2 4 a c 2 a Integration by parts: a b f x g ' x dx = f x g x ] a b a b f ' x g x dx...
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This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.

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