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01 (a) Show that the rst-order differential equation 39'4ny = 0 can be obtained by using: (i) separating-variable method, and (2 marks) (ii) power series

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01 (a) Show that the rst-order differential equation 39'4ny = 0 can be obtained by using: (i) separating-variable method, and (2 marks) (ii) power series method without using recurrence relations. (8 marks) (b) Solve using power series method for the given second-order differential equation with initial condition 91(0) = 0. 9"0) + 59'0) = 40 (10 marks)

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