(25 points) Consider the following initial value problem, in which an input of large amplitude and short duration has be

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25 Points Consider The Following Initial Value Problem In Which An Input Of Large Amplitude And Short Duration Has Be 1 (37.74 KiB) Viewed 47 times

(25 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" – 7y' = (t – 2), y(0) = 6, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). g(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0 <t <2, g(t) = if 2 <t<o.