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a For what values of r does the function y e satisfy the differential equation...

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Calculus

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a For what values of r does the function y e satisfy the differential equation 5y 34y 7y 0 Enter your answers as a comma separated list r b If r and r are the values of r that you found in part a show that every member of the family of functions y ae 1 be 2 is also a solution Let 1 be the larger value and r be the smaller value We need to show that every member of the family of functions y ae 1 be 2 is a solution of the differential equation 5y 34y 7y 0 We must decide whether 5f x 34f x 7f x 0 for f x ae 1X be 2x Substitute your values for r and r into f x then find f x and f x We have f x and f x Substituting and combining like terms we get the following C De x Therefore f x ae1 be 2 is a solution to the differential equation 5y 34y 7y 0 5f x 34f x 7f x

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