Question: Consider the initial value problem2xy=4y,y(1)=2. 1) Find the value of the constant C and the exponent r so that y = C x r is

Consider the initial value problem2xy=4y,y(1)=2.

1) Find the value of the constantCand the exponentrso thaty=Cxris the solution of this initial value problem

2) Determine the largest interval of the forma<x<bon which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

3) It can happen that the interval predicted by the Fundamental Theorem is smaller than the actual interval of existence. What is the actual interval of existence in the forma<x<bfor the solution (from part 1)?

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