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" - 3y' + 2y = 0; y₁ = e^x, y₂ = e^2x; y(0) = 1, y'(0) = 0