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# 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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