Question: (a) Find an implicit solution of the IVP (2y + 2)dy - (4x 3 + 6x)dx = 0, y(0) = -3. (b) Use part (a)

(a) Find an implicit solution of the IVP

(2y + 2)dy - (4x³ + 6x)dx = 0, y(0) = -3.

(b) Use part (a) to nd an explicit solution y = -(x) of the IVP.

(c) Consider your answer to part (b) as a function only. Use a graphing utility or a CAS to graph this function, and then use the graph to estimate its domain.

(d) With the aid of a root finding application of a CAS, determine the approximate largest interval I of definition of the solution y = φ(x) in part (b). Use a graphing utility or a CAS to graph the solution curve for the IVP on this interval.

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