Question

Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a snaar point at x 0 . It the singular point at x-0 is a regular singular point, then a power series for the solution y(x) can be lound using the Frobenius method. Show that x = 0 is a regular sigar point by calculating: xp(x) = y(x) = Since both of these functions are analytc atx-0 the singular point is regular (b) Enter the indicial equation, in terms of r, by filling in the blank below (c) Enter the roots to the indicial equation below. You must enter the roots in the order of smallest to largest, separated by a comma. (d) You must now calculate the solution for the largest of the two ndicial 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: arnis entered as a (m),amr+1 asa(n. 1) , etc. (e) Hence enter the first three non-zero terms of the solution corresponding to the largest indicial root Note: The syntax for a and a is ad and al, respectively. 自監

Answer 1

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