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Unformatted text preview: 3. (a) (10 points) Show that the following equation is exact: 2 x + y 2 + 2 xy dy dx = 0 (b) (10 points) Find the explicit solution to the initial value problem: 2 x + y 2 + 2 xy dy dx = 0 , y (1) = 1 4. (20 points) Find an integrating factor for the following equation (you do not need to solve the equation): 4 x 2 y + 2 y 2 + (3 x 3 + 4 xy ) dy dx = 0 Hint: It is of the form ( x, y ) = xy a for some a . 5. (10 points) Solve the initial value problem: dy dx = sin( y )(2 y4)( y 36 y 2 + 12 y8) , y (1) = 2 6. (10 points) Find the equilibrium solutions for the following equation, and identify them as asymptotically stable or unstable. dy dt = y 25 y + 6 Extra Scratch Paper:...
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 Fall '07
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 Math, Differential Equations, Equations

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