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Unformatted text preview: Muhammad Ulhaque Assignment 2 MATH263, Winter 2008 due 1/27/08 at 11:55 PM. 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 5 x 2 1 y 2 x 3 ? y dy dx 5 x 2 2 ? dy dx ln y ln x ? x 2 dy dx 3 x 2 2 y 2 ? dy dx 2 xy 3 x 3 Correct Answers: LINEAR SEPARABLE HOMOGENOUS HOMOGENOUS LINEAR 2. (1 pt) By using the substitution z 2 x y 3 (you are to replace the pair x y with the pair x z ) solve the initial value problem y 9 2 x y 3 2 23 y 3 The solution is y x = . The largest interval on which the solution is valid is x . Enter INF for and NEGINF for . Correct Answers:-(75*x-69*x-9-5*tan(15*x))/3-0.10471975511966 0.10471975511966 3. (1 pt) Consider the implicit differential equation 45 y 3 22 xy dx 50 xy 2 12 x 2 dy Show that x p y q is an integrating factor of this equation where...
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- Spring '08