(a) Verify that 3x 2 y 2 c is a one parameter family of solutions of the differential equation y dy dx 3x (b) By hand, sketch the graph of the implicit solution 3x 2 y 2 3 Find all explicit solutions y (x) of the DE in part (a) defined by this relation Give the interval I of definition of each explicit solution (c) The point (2, 3) is on the graph of 3x 2 y 2 3, but which of the explicit solutions in part (b) satisfies y(2) 3

Question: (a) Verify that 3x 2 y 2 = c is a one-parameter family of solutions of the differential equation y dy/dx = 3x. (b)

(a) Verify that 3x² y² = c is a one-parameter family of solutions of the differential equation y dy/dx = 3x.

(b) By hand, sketch the graph of the implicit solution 3x² y² = 3. Find all explicit solutions y = ϕ(x) of the DE in part (a) defined by this relation. Give the interval I of definition of each explicit solution

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