Question

Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimas. (a) The above differential equation has a singular point at z-0.I the singular point at z -0 is a regular singular point, then a power series for the solution ()can be found using the Frobenius method. Show that z-O is a regular singular point by calculating plz)-3 Since both of these functions are analytic at r -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 0,4 (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 n as your index. Note 3: am is entered as(m) a+1 a(1), etc e) Hence enter the first three non-zero terms of the solution corresponding to the largest indicial root Note: The syntax for ag and a1 is ao and a1, respectively

Answer 1

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