Assignment #3 - Stephanie Campbell due at 11:55pm EDT...

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Stephanie Campbell Assignment 3 MATH263, Fall 2010 due 09/30/2010 at 11:55pm 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 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 ( 0 ) = 6 The solution is y ( x ) = . The largest interval on which the solution is valid is < x < . Enter INF for and NEGINF for - . 3. (1 pt) Consider the implicit differential equation ( 15 y 3 + 14 xy ) dx +( 42 xy 2 + 20 x 2 ) dy = 0 Show that x p y q is an integrating factor of this equation where p = and q = .
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