If the given solutions ÿ₁ (t) = 2e³-8e-1 3e3-20e-t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem ÿ₂(t) = ÿ(t) = (0) 8e³+2e-t [12e³t+5e-t] ÿ, ÿ(0) = [1]. impose the given initial condition and find the unique solution to the initial value problem. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2e3-8e-17 [ 3e ³ = 20e-1] + (0) 8e³+2e7 12est +5e7 1

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