In 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 particularsolution of the form y = C1y1 + y = C2y2 that satisfies the giveninitial conditions. Primes denote derivatives with respect to x.
y″ + 2y′ + y = 0; y1 = e−x, y2 = xe − x; y(0) = 2, y′(0) = −1
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