exam1_ODE - Name UF ID number Exam 1 MAP 2302 Fall’11...

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, 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....
View Full Document

This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online