Question: 1. For the differential equation, 3'! + 2y = 4 t+6 with initial condition of y(0) = 3, find ylt) a. by using the analytic

1. For the differential equation, 3'! + 2y = 4 t+6 with initial condition of y(0) = 3, find ylt) a. by using the analytic method (20 points) b. by using finite difference numerical method and selecting a proper step time for the first 3 values of yi. (20 points) c. by using the Laplace transform, (20 points) d. compare results of part a, b, and c, give your comment. (10 points)

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