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Unformatted text preview: 5 (4) Find the general solution of d 2 y dt 2 + 2 dy dt + αy = 0 , where α is some positive constant. Your answer should be valid for all possible choices of α > 0. 6 (5) Find the general solution of d 2 y dt 2 + 3 dy dt + 2 y = cos t. 7 Do either this problem or problem 3 (on complex numbers) but not both (6) (a) Find the equation in Cartesian Coordinates for the curve which in Polar Coordinates is given by r 2 = sin θ cos θ . (b) Find the equation in Polar Coordinates for the curve which in Cartesian Coordinates is given by x 4 + y 2 = 3 x . (c) Consider a Logarithmic Spiral which in Polar Coordinates is given by r = e θ/ 2 π . For which value(s) of θ between 0 and 2 π does this spiral have a horizontal tangent? [Continue on reverse side, if necessary]...
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 Fall '08
 Wilson
 Math, Calculus, Geometry, Cartesian Coordinate System, Complex number, Polar coordinate system

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