Problem 1- Solve y'' + y' = 2 sinx - 4 cosx.

Problem 2- The temperature outside is 40oF. A 120oF liquid is carried outside. One minute later, the temperature of the liquid has dropped to 100oF. What is the exact temperature of the liquid 2 minutes after being taken outside?

Problem 3- Solve (x2y - 2y3) dx = x3dx explicitly as a function of y alone.

Problem 4- Using Laplace transforms, solve

u'' - v' = 5

u' + v'' = -6

subject to

u(0) = -2, u'(0) = 1

v(0) = 4, v'(0) = -1.

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