Unformatted text preview: (a) dy dx = e x + y , y (0) = 0. (b) y ′ ( t )t ( y ( t )) 2 = t (general solution). 4. (8 points) Write down an integral in polar coordinates for the area of the region that lies inside the curve r = 2cos θ and outside the curve r = √ 2. 5. (6 points) Consider the diFerential equation y ′ ( t ) = 1y 2 . ±ind the limiting behavior of y ( t ) (that is, what is lim t → + ∞ y ( t )) if the initial condition is (a) y (0) = 0 (b) y (0) = 2. You do not need to solve the equation — a clear explanation in a few words will su²ce. END O± EXAM...
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 Fall '08
 Justin
 Math, Calculus, Logarithm, blue book, MATH 20B

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