Problem 2. (a) Use the fact that 3x2 − y2 = c is a one-parameter family of solutions of the differential equation y =3x

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Problem 2.
(a) Use the factthat 3x2 − y2 = c isa one-parameter family of solutions of the differentialequation
y
=3x
= 3x to find an implicit solution of theinitial-value problem
y
= 3x, y(2) = −6.
(b) Give the interval I of definition ofthe explicit solution. (Enter your answer using intervalnotation.)
(c) Are there any explicit solutions of
y
= 3x
that pass through the origin? (If yes, enter the explicitsolutions as a comma-separated list. If not, enter NONE.)