Consider the two-parameter family of functions defined by
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Consider the two-parameter family of functions defined by y=C1e2x+C2e−2x, where C1 and C2 are arbitrary real constants.
(1) Part 1: Compute the first and second derivatives of the general member of the family.
(2) Part 2: Show that every member of the family satisfies the relation y′′−4y=0.
(3) Part 3: Give a clear argument that the differential equation obtained in part (b) is of the lowest possible order for which all members of the given family are solutions.