2. Consider the first order initial value problem dc + 1 = f(t) dt where x(0) = 5 and the function f is defined by = 2 c

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2 Consider The First Order Initial Value Problem Dc 1 F T Dt Where X 0 5 And The Function F Is Defined By 2 C 1 (48.45 KiB) Viewed 18 times

2. Consider the first order initial value problem dc + 1 = f(t) dt where x(0) = 5 and the function f is defined by = 2 cos(3), 0 <t<n, f(t) = 5et, t> (a) Sketch f over the range 0) <t<27. (b) Write f in terms of unit step functions. Hence find the Laplace transform of f. (c) Solve the initial value problem using i. Laplace transforms, ii. dsolve in MATLAB. (d) Verify that your analytical solution and MATLAB solution in part (C) are equivalent.