M427K Exam IB
Spring 2014
(prmt) Name_
BID"
NO NOTES. NO CALCULATORS.
1. Find the general solution of y' + 2y = t
at.
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2. A tank contains 60 pounds .of salt dissolved in 500 gallons of water. A solution of 2 pounds of salt per gallon is
pumped into the tank at a rate of 5 gallons per minute! The well-mixed solution is drained from the tank at a rate
of 2 gallons per minute. Write an IVP whose solution is the number of pounds of salt in the tank at time t. Do not
solve the IVP. Please do not ask whether the previous sentence means that you should not solve the IVP.
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3. Find the Largest intgryaLover which the IVP cos(t)y' + y = et, y(4) = 7 has a unique solution.
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4. Solve the IVP (x + siny) dx + (xcosy - 1y) dy = 0, j/(0) = 2.
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5. Use Picard'sjnethod with fa = 0 to find fa for the IVP y' = ty + 3, y(0) = 0.
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6. Find and classify the equilibrium solutions of y' = (y — 4)(y + 2)2 and sketch a few representative trajectories
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