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We will solve the initial value problem using the Laplace transform. ### Given differential equation: \[ y'' - 2y' - 3y = 0 \] with initial conditions: \[ y(0) = 1, \quad y'(0) = 7 \] #### Step 1: Take the Laplace Transform Using the properties of Laplace transforms: \[ \mathcal{L}\{y''(t)\} = s^2 Y(s) - s y(0) - y'(0) \] \[ \mathcal{L}\{y'(t)\} = _____ ____ _____ _______ ____ ___ ________ ____ _________.
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