10Ma2aAnHw4 - 1 2 , and that at any time the goose is...

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Ma 2a Fall 2010 (analytical track) PROBLEM SET 4 Due on Monday, October 25 I. Integration of 1st order equations (X1) Solve the equation ˙ x = t t 2 x + x 3 (Hint: s = t 2 ) . (X2) Solve the initial value problem y 0 = y 3 1 - 2 xy 2 , y (0) = 1 . II. 2D autonomous systems and reducible 2d order equations (X3) Solve the equation y 00 + ( y 0 ) 2 = 2 e - y . (X4) A goose attempts to fly back to its nest, which is directly west of its position, but a steady wind is blowing from the southeast. Find the flight path assuming that the speed of the goose is 1, the speed of the wind is
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Unformatted text preview: 1 2 , and that at any time the goose is heading to its nest. Also, nd the ight time. (Can the goose get home in nite time?) III. 2d order linear equations with constant coecients Problem 12.1 (vii) Problem 14.1 (xi) [Use the reduction of order method] Problem 18.1 (ii) [Use the variation of constants method] IV. 2d order dierence equations Problem 22.1 (iv) Midterm will be available 10/25 and will be due 11/1 1...
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