Question: (a) Verify that the one-parameter family y 2 2y = x 2 x + c is an implicit solution of the differential equation

(a) Verify that the one-parameter family y² 2y = x² x + c is an implicit solution of the differential equation (2y 2)y' = 2x 1.

(b) Find a member of the one-parameter family in part (a) that satisfies the initial condition y(0) = 1.

(c) Use your result in part (b) to find an explicit function y = ϕ(x) that satisfies y(0) = 1. Give the domain of the function ϕ. Is y = ϕ(x) a solution of the initial-value problem? If so, give its interval I of definition; if not, explain

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a Differentiating y 2 2y x 2 x c we obtain 2yy 2y 2x1 or 2y 2y 2x1 b Setting x 0 and y 1 in the so... View full answer

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