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Unformatted text preview: v ( t ) for any t > 0 (up until the object strikes the ground). Show v ( t ) approaches a limit as t . 4. ( Linear Dierential Equations ) Solve the dierential equations in parts (a)(b) (a) dy dx-2 y x = x 2 , y (1) = 2 (b) x dy dx-4 y = x 5 e x , y (1) = e 5. (a) A Bernoulli dierential equation is of the form dy dx + P ( x ) y = Q ( x ) y n Observe that if n = 0 or n = 1, the Bernoulli equation is linear. For other values of n , show that the substitution u = y 1-n transforms the Bernoulli equation into the linear equation du dx + (1-n ) P ( x ) u = (1-n ) Q ( x ) (b) Use the method in part (a) to solve the dierential equation dy dx + 2 x y = y 3 x 2...
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.
- Fall '08