# Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y =...

Question 3 Consider the ordinary differential equation (ODE) 2xy" + (1 + x)y' + 3y = 0, in the neighbourhood of the origin. a) Show that x = 0 is a regular singular point of the ODE. (10) b) By seeking an appropriate solution to the ODE, show that G=- (10) i) the roots to the indicial equation of the ODE are 0 and 1/2. [10] ii) the recurrence formula used to determine the power series coefficients, ens when one of the indicial equation roots is 1/2 is given by 7.00 (28+7) Cs+1 s = 1,2,..... (28+3)(8+1) iii) For the indicial equation root 1/2, show that one of the solutions to the ODE IS given by y = cova[1 -+ 21x2_77x (5) 40 560

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