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Unformatted text preview: Stephanie Campbell Assignment 3 MATH263, Fall 2010 due 10/01/2010 at 04:00pm EDT. Please note that you have a limit of 6 tries for all problems on this assignment. 1. (1 pt) Determine the type of each ODE from among the types ’linear’, ’separable’ and ’homogenous’ . Please note that in this question by homogenous, we mean equations of the form dy dx = F ( x- 1 y ) not linear equations with zero forcing function (linear homoge- nous equations). ? x dy dx = x 2 + y ? x dy dx = 4 ( x 2 + 1 ) y- 6 x 3 ? dy dx = ln ( y )- ln ( x ) ? y dy dx = 4 x 2 + 6 ? dy dx = 6 xy + 7 x 3 Correct Answers: • linear • linear • homogenous • separable • linear 2. (1 pt) By using the substitution z = 2 x + y- 6 (you are to replace the pair ( x , y ) with the pair ( x , z ) ) solve the initial value problem y = 4 ( 2 x + y- 6 ) 2 + 14 , y ( ) = 6 The solution is y ( x ) = . The largest interval on which the solution is valid is < x < ....
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- Fall '09
- Math, Stephanie Campbell