(a) Use implicit differentiation to show that t2 – 4y2 = C2 implicitly defines solutions of the differential equation t –4yy' = 0.
(b) Solve t2– 4y2 = C2 for y in terms of t to provide explicit solutions. Show that these functions are also solutions of t– 4yy' = 0.
(c) Discuss the interval of existence for each of the solutions in part (b).
(d) Sketch the solutions in part (b) for C = 1, 2, 3, 4.
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