(a) Verify that 3x2 − y2 = c is a one-parameter family of solutions of the different...

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

(b) By hand, sketch the graph of the implicit solution 3x² − y² = 3. Find all explicit solutions 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?