# ps4 - 2 For each of the following Euler equations ﬁnd the...

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Problem Set 4 February 9, 2007 Due February 16, 2007 ACM 95b/100b 3pm in Firestone 303 Niles A. Pierce (2 pts) Include grading section number 1. Consider the following initial value problem with variable coeﬃcients y 00 + xy 0 + 2 y = 0 , y (0) = 4 , y 0 (0) = - 1 . a) (10 pts) Find the recurrence relation for the coeﬃcients in a power series solution expanded around x 0 = 0. b) (12 pts) Find the ﬁrst three nonzero terms of each of the linearly independent solutions. c) (10 pts) Set the two constants to satisfy the initial conditions and plot several approximations to y ( x ) for diﬀerent truncations of the series solution.
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Unformatted text preview: 2. For each of the following Euler equations, ﬁnd the general solution valid except at the regular singular point. a) (10 pts) x 2 y 00-xy + y = 0 b) (10 pts) ( x-1) 2 y 00 + 8( x-1) y + 12 y = 0 3. For each of the following linear diﬀerential equations, use the method of Frobenius to ﬁnd two linearly independent solutions expanded about the regular singular point at x = 0. a) (40 pts) xy 00 + y-y = 0 b) (40 pts) x 2 y 00 + xy + ± x 2-1 4 ² y = 0 Total points: 134...
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## This note was uploaded on 11/23/2009 for the course ACM 95b taught by Professor Nilesa.pierce during the Winter '09 term at Caltech.

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