exam1_ODE - Name : UF ID number : Exam 1, MAP 2302, Fall11...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name : UF ID number : Exam 1, MAP 2302, Fall11 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 /dt 2 + 2 = 0 where 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....
View Full Document

Ask a homework question - tutors are online