Differential_Equations_Practice

Differential_Equations_Practice - Dierential Equations...

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Differential Equations Practice 1. Suppose that y ( x ) is a function which is never zero and satisfies the differential equation - y 0 = 2 xy 2 . Suppose also that y (0) = 3. Find y . 2. Is it possible that y 2 + ( y 0 ) 2 = 1? If not, explain why. If so, give an example. 3. Revolve the region in the first quadrant bounded by the graph of the function y = - x 2 + h , h > 0, about the y -axis. The 3-dimensional solid obtained is the shape of a melting heap of snow when it is of height h . (a) Express the volume V of the heap of snow as a function of its height h . (b) The heap of snow melts at a rate equal to the area of its base. What is the rate at which its height is decreasing? ( Hint: ‘Rate’ means derivative. Solve for dh dt using what you know about dV dt .) (c) Assuming that h = 60 when t = 0, what is the rate of melting when t = 50? 4. The third-life of a radioactive element is defined to be the time required for two thirds of the radioactive
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