Consider the following first-order initial value problem involving the function x(t): dx/dt = ax + u(t),

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2. Consider the following first-order initial value problem involving the function x(t): dx dt = ax + u(t), x(0) = x0 , (1) where a E R is a constant and u(t) is an arbitrary function defined for t > 0. (a) Find the solution x(t) of this first order DE in terms of a definite integral involving u(s) over s E [0, t]. You can solve the DE using an integrating factor. (b) Find the same solution using the Laplace transform applied to the DE