Let $y(t)$ solve the initial value problem $\dot{y}(t) + 8y(t) = u_4(t)f(t-4); y(0) = 0$
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First, we need to find the Laplace transform of the given equation. The Laplace transform of y'(t) is sY(s) - y(0), and the Laplace transform of y(t) is Y(s). Since y(0) = 0, we have: L{y'(t) + 8y(t)} = L{34f(t-4)} sY(s) - 0 + 8Y(s) = 34F(s)e^{-4s} Show more…
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