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" - 10y' + 25y = 0; y1 = e5x, y2 = xe5x; y(0) = 3, - y' (0) = 13

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