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ch01_2 - Ch 1.2 Solutions of Some Differential Equations...

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Ch 1.2: Solutions of Some Differential Equations Recall the free fall and owl/mice differential equations: These equations have the general form y' = ay - b We can use methods of calculus to solve differential equations of this form. 450 5 . 0 , 2 . 0 8 . 9 - = - = p p v v

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Example 1: Mice and Owls (1 of 3) To solve the differential equation we use methods of calculus, as follows. Thus the solution is where k is a constant. 450 5 . 0 - = p p ( 29 C t C t C t e k ke p e e p e p C t p dt p dp p dt dp p dt dp ± = + = ± = - = - + = - = - = - - = + , 900 900 900 5 . 0 900 ln 5 . 0 900 5 . 0 900 / 900 5 . 0 5 . 0 5 . 0 5 . 0 t ke p 5 . 0 900 + =
Example 1: Integral Curves (2 of 3) Thus we have infinitely many solutions to our equation, since k is an arbitrary constant. Graphs of solutions ( integral curves ) for several values of k , and direction field for differential equation, are given below. Choosing

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ch01_2 - Ch 1.2 Solutions of Some Differential Equations...

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