Question

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3) For thè diferential equation: (a) The point zo =-1 is an ordinary point. Compute the recursion formula for the coefficients of the power series solution centered at zo- -1 and use it to compute the first three nonzero terms of the power series when -1)-s and v(-1)-0. (25 points) (b) The point z = 0 is a regular singular point . Compute the associated Euler equation and compute the recursion formula for the coefficients of the series solution centered at zo = 0 which is associated with the smaller root. (20 points)

3) For thè diferential equation: (a) The point zo =-1 is an ordinary point. Compute the recursion formula for the coefficients of the power series solution centered at zo- -1 and use it to compute the first three nonzero terms of the power series when -1)-s and v(-1)-0. (25 points) (b) The point z = 0 is a regular singular point . Compute the associated Euler equation and compute the recursion formula for the coefficients of the series solution centered at zo = 0 which is associated with the smaller root. (20 points)

Answer 1

age- 2. which ard anaay tic at ~o=-1 . Honea ot C2) Diasre ntiating (2) twice in successi on 一13) Putting thes aQuos on Y, yland Ylin uation, we get

n=2 Y1ゥ! 0o 0o heo วา วา

sincQ (4) is an dentity. aguating the Constent toim and the caossicient os od ㅈto 22ho / a0.9见七 4.3

12 '11で 12 24 24 24 Page-y 24 Putting the above va axes。よG,G, Cy in (2) Putting the above vadu es。ơ c2,C3) 2. 24 3 Hence Ans 2 1

Answer 2

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