341hw3 - 1 dx dt = x-4 2 dx dt = 3-x 3 dx dt = x-2 2 For...

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Homework 3, due Friday September 23rd , in class For questions 1 to 3, (i) Find all critical points of the given (autonomous) differential equation. (ii) By analyzing the sign of the right-hand side, classify each critical point as stable or unstable. (iii) Solve the differential equation explicitly. (iv) Find the particular solutions for initial values “close” to the critical points, such as x = 3 . 9 and x = 4 . 1 in Question 1.
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Unformatted text preview: 1. dx dt = x-4 2. dx dt = 3-x 3. dx dt = ( x-2) 2 For questions 4 and 5, (i) Verify that the given functions are solutions of the differential equation. (ii) Find the particular solution that satisfies the given initial conditions. 4. y 00-9 y = 0; y 1 = e 3 x , y 2 = e-3 x ; y (0) =-1 , y (0) = 15 5. y 00 + 4 y = 0; y 1 = cos 2 x, y 2 = sin 2 x ; y (0) = 3 , y (0) = 8...
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This note was uploaded on 12/07/2011 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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