Question: homogeneous second order differential equation 7. This question is about solving the homogeneous, second-order differential equation y - 2xy' - 2y = 0. (a) Using

homogeneous second order differential equation

7. This question is about solving the homogeneous, second-order differential equation y" - 2xy' - 2y = 0. (a) Using a power-series expansion about x = 0 find the recurrence relation for the coefficients of this ODE. You do not need to solve the recurrence. [12 marks] (b) Find the values of the first 3 non-zero terms of the recurrence satisfying the conditions y(0) = 1 and y'(0) = 0. Hint: try the series solution with do = 1; a] = 0. [6 marks] (c) Confirm by substitution that y(x) = exp(x2) is a solution of the ODE. [4 marks]

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