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MATH 225 LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS HOMEWORK 1 Due February 21-26 before the lecture starts. For sections 1, 3 &4; February 23, Wednesday; for section 2; February 24, Thursday. 1) Solve the differential equation 1 sin 1 cos = + y x dx dy y by using the substitution . sin y v = 2) Solve the initial value problem = + = + + 4 ) 0 ( 2 ) ( 2 1 y x x f y x dx dy , where < = 2 , 4 2 0 , 2 ) ( x x x x f . 3) Consider the differential equation ( ) . 0 2 2 2 = - + dy x dx xy y a) Show that this equation is not exact. b) Multiply the given equation through by n y , where n is an integer, and then determine n so that n y is an inregrating factor of the given equation. c) Multiply the given equation by the integrating factor found in part
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Unformatted text preview: b) and Solve the resulting exact equation. 4) A certain city had a population of 25,000 in 1960 and a population of 30,000 in 1970.Assume that its population will continue to grow exponentially at a constant rate.What population can its city planners expected in the year 2020? 5) Suppose that you discover in your attic an overdue library book on which your grandfather owed a fine of 30 cents 100 years ago. If an overdue fine grows exponentially at a 5% annual rate compounded continuously, how much would you have to pay if you returned the book today?...
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