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dy Consider the 2nd-order ODE dy + (1+r) + 2y = 0. dac (a) A Frobenius series solution yı() takes the form C d22 yı(x) =
Posted: Wed May 11, 2022 9:12 pm
by answerhappygod
- Dy Consider The 2nd Order Ode Dy 1 R 2y 0 Dac A A Frobenius Series Solution Yi Takes The Form C D22 Yi X 1 (80.87 KiB) Viewed 18 times
dy Consider the 2nd-order ODE dy + (1+r) + 2y = 0. dac (a) A Frobenius series solution yı() takes the form C d22 yı(x) = axxk+c, k=0 with ao #0 and CER. Compute the indicial equation for c. Determine a recurrence relationship for the ak and thus deduce an explicit expression for as in terms of ao. Page 1 of 3 (b) A second linearly independent solution to the ODE can be written as y2(x) = yı (x) log 1 + bkxk+c k=1 Show that bk = ax + + 1 k+1 for some ; that you should determine. You may use any theoretical results from the lectures as long as they are stated clearly. (c) Suppose solutions y(1) of the ODE are bounded at r = 0) and satisfy dhy =1, drn for some positive integer n. Determine y(0) in this case. . [—四