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Homework for §1.4 Find general solutions (implicit if necessary, explicit if convenient) of the differential equations below. Primes denote derivatives with respect to x. dy + 2xy 2 = 0 dx dy 2. (1 − x2 ) = 2y dx dy 3. y 3 = (y 4 + 1) cos x dx ............................................................................. 1. Find an explicit particular solution to the initial value problems below. π π dy = y, y = 4. (tan x) dx 2 2 dy 5. = 6e2x−y , y(0) = 0 dx ............................................................................. 6. 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? 7. A cake is removed from the oven at 210◦ F and left to cool at room temperature, which is 70◦ F . After 30 minutes the temperature of the cake is 140◦ F . When will it be 100◦ F ?