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(1 point) Consider the initial value problem 2xy = 8y, y( 1 ) =-2. 1) Find the value of the constant C and the exponent r so that y = Cx, is the solution of this initial value problem. Hint: To find r plug y = Cx, into the equation and simplify. Then to find C apply the initial condition. help (formulas) The Fundamental Existence Uniqueness Theorem for First Order Linear IVPs states: Given the IVP problem ai (x)y aoyg(x) y(xo)yo, assume that a, aog are continuous on an interval a < x < b with a < Xo < b and with ai (x) 0 for all a <x <b. Then there exists a unique solution on the whole interval a<x <b. 2) Determine the largest interval of the form a <x <bon which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution. a <x <b is help (inequalities) 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 form a< x <b for the solution (from part 1)? a <x <b is help (inequalities)
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