Unformatted text preview: Name : UF ID number : Exam 1, MAP 2302, Fall’11 Show your work! Write your name on every piece of paper you turn in! 1 . Find all solutions of dy dx = 4 x radicalBig y- 1 . Hint : Analyze the uniqueness! 2 . Solve the initial value problem: (3 x 2 y + 2 x ) dx + ( x 3 + 3 y 2 ) dy = 0 , y (1) = 1 . 3 . Identify the type of the differential equation and solve the initial value problem: dy dx + 2 xy = e x 2 y 2 , y (0) = 1 . 4 . Transform the equation to a separable equation and then find its general solution ( x- y- 2) dx + ( x + y ) dy = 0 5 . If y 1 ( x ) = e- x is a solution of y primeprimeprime- y primeprime + 2 y = 0 find its general solution. Hint : What is the root of the characteristic equation that corresponds to y 1 ? 6 . The pendulum equation is d 2 θ/dt 2 + ω 2 θ = 0 where θ is the deviation angle from the equilibrium position and t is time. In reality, the pendulum cannot move forever because there is a drag (friction) force. If the drag force is added, then the pendulum equation becomes:is a drag (friction) force....
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