[5 marks] 3. Consider the following differential equation (4 − t²)y" + 2y = 0 ∞ and a series solution to the differentia

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5 Marks 3 Consider The Following Differential Equation 4 T Y 2y 0 And A Series Solution To The Differentia 1 (86.78 KiB) Viewed 47 times

[5 marks] 3. Consider the following differential equation (4 − t²)y" + 2y = 0 ∞ and a series solution to the differential equation of the form Σant". n=0 (a) Find the recurrence relations for the coefficients of the power series. [3 marks] [1 mark] (b) Determine the radius of convergence of the power series. (c) Write the first eight terms of the series solution with the coefficients written in terms of ao and a1. [2 marks]