Question: In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y 1 and y 2 , and a pair of initial conditions

In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions y1 and y2, and a pair of initial conditions are given. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.

y" + y' - 6y = 0; y1 = e2x, y2 = e-3x; y(0) = 7, y' (0) = -1

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