(a) Verify that 3x2 y2 c is a one-parameter family of solutions of the differential

Chapter 1, Problem 33

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(a) Verify that 3x2 y2 c is a one-parameter family of solutions of the differential equation y dydx 3x. (b) By hand, sketch the graph of the implicit solution 3x2 y2 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 3x2 y2 3, but which of the explicit solutions in part (b) satisfies y(2) 3? 34

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