MATH 285 E1 F1 GRADED HOMEWORK SET 2 DUE FRIDAY SEPTEMBER 26 IN LECTURE LET S CHANGE IT UP WITH SOME FRESH NEW INSTRUCTIONS This time the homework has two parts A and B Please turn in each part separately with your name and section clearly marked on each part Please staple all the pages for a particular part together but do not staple the two parts to each other When you turn the homework in there will be two boxes Thank you Part A 1 5 points Consider the equation dy x yexy 0 dx Show that this equation is exact and find an implicit equation for the solution 2 5 points Let P t denote the number of technology startups in the San Francisco Bay area where time t is measured in months Startups are created when two recent graduates decide to found one and they either fail or they are bought by Google The rate at which startups are formed is given by 10 0 01P P per month Also each month 10 of the startups fail and 5 are bought by Google How many startups do you expect to exist at a particular time many months into the future That is what is limt P t 2y xexy Part B 3 5 points Suppose that y1 x and y2 x are two solutions of the nonhomogeneous equation A x y 00 B x y 0 C x y F x Prove that their difference y1 x y2 x is a solution of the homogeneous equation A x y 00 B x y 0 C x y 0 4 15 points a Find the general solution of the second order linear homogeneous equation 4y 00 8y 0 3y 0 1 2 GRADED HOMEWORK 2 b Using your innate cleverness find a particular solution to the nonhomongeneous equation 4y 00 8y 0 3y 15 c Using the results of the previous two parts find solution of the initial value problem 4y 00 8y 0 3y 15 y 0 0 y 0 0 0
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