Question

Conslder the following differentlal equatlon, Note: For each part below you must give your answers in terms ot fractions (as appropriate), not decimals. (a) The above ditferential equation has a singular point at0. If the singular point at-0 is a regular singular point, then a power series for the solution y) can be found using the Frobenius method. Show that -0 is a regular singular point by calculating pa)2 Since both of these functlons are analytlic at regular the singular polnt Is (b) Enter the indlclal equation, In terms of r, by fillilng In the blank below. r*2-3*r (c) Enler lhe raals lo Ihe indicial equalion belaw. You musl enler lhe rools in lhe order of smallesl s separaled by a camma. 0,3 (d) You must now calculate the solution for the largest of the two indicial roots. First, enter the corresponding recurrence relation below, as an equation Note 1: You must include an equals sign. Note 2: You must use the symbol m as your index. Note 3: am is entered as a (m), am+1 as a (m+1), etc. (e) Hence enter the first three non-zero terms of the solution corresponding to the largest indicial root. Note: The syntax for an and aj is ao and a1, respectively.

Answer 1

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