Pratice quiz 1 - quizz PDF

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Math 3041

Practice Quiz 1

May 10, 2016

1.

Without actually solving the differential equation y′ = 2y − 5 , (a) find the equilibrium solution(s), and (b) in each region of the plane determined by them, determine whether the solution curves are increasing or decreasing and whether they are concave up or concave down. (c) Illustrate your results graphically.

2.

Repeat Problem 1 for y′ = y( y − 6) .

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3. Solve the initial-value problem y′ = 2y − 5, y(0) = 3, and find lim y(t) . t →∞

4.

Find the solution of y′ = y( y − 6) for each of the following initial conditions. (b) y(0) = 3 (c) y(0) = 7 (a) y(0) = −1

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5.

A 200 L tank initially contains 100 g of a chemical. A solution containing 0.5 g/L of the same chemical flows into the tank at the rate of 6 L/min, and the well stirred solution flows out at the same rate. (a) How much chemical is in the tank at time t? (b) What would be the differential equation for the amount of chemical in the tank if solution were flowing out at the rate of 8 L/min?

6.

Newton’s law of cooling says that the temperature T (t) of an object at time t (measured in hours) satisfies the differential equation dT dt = −r(T − A) , where r is a positive constant, and A is the ambient temperature. Suppose T (0) = 70 F , T (1) = 100 F , and A = 350 F . Find t1 for which T (t1) = 145 F .

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