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Solve the initial value problem?

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1 Answer

Here we have 2 distinct roots to the characteristic equations r = -1, 2 so the general solution becomes:

y(t) = C1e-t + C2e2t

plugging in our initial conditions we get:

y(0) = C1 + C2 = a

y'(0) = -C1 + 2C2 = 2

After solving this 2 X 2 linear system (preferably using the elimination method) we should get C1 = 2(a-1)/3 and C2 = (a+2)/3.

since e2t → ∞ as t → ∞ we need to force that C2 = 0, doing so gets you a = -2

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