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2. Reduction of order/undetermined coefficients/series solutions (a) _ _ Consider the ODE xzy\" xy' + y = O. i. Verify that y1(x) = x is one solution to this ODE. ii. Using the method of reduction of order find the second solution to this ODE. (b) _ _ Consider the inhomogeneous ODE y\" 4}; = 8. Using the method of undetermined coefficients find the general solution to this ODE by: i. Find the general solution to the homogeneous problem. ii. Find a particular solution to the inhomogeneous problem. (c) Consider the topic of series solutions to an ODE. i. Briefly describe the notion of a regular singular point for an ODE. (Two sentences/equations would be sufficient.) ii. Briefly describe the notion of a Frobenius series, and indicate how one might find the Frobenius exponent. (Two sentences/equations would be sufficient.)