Question: Problem 2: (i) Let f(t) be a real-valued function for t0. Detine the Leplece fransform C[f] of f.(ii) Compute L[c4t4t5-sin2(3t)].(iii) Solve the differential equation y''-2y'-8y=24t6,y(0)=1,y'(0)=-5

Problem 2: (i) Let f(t) be a real-valued function for t0. Detine the Leplece fransform C[f] of f.(ii) Compute L[c4t4t5-sin2(3t)].(iii) Solve the differential equation y''-2y'-8y=24t6,y(0)=1,y'(0)=-5 using the method of Laplace transforms.

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