This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: NAME Quiz II
y 1. a) The differential form = (ln y + x  1)dx + (ln x + x  1)dy is exact in any y rectangle contained in the first quadrant (where x > 0 and y > 0). Find a function F (x, y) defined in the first quadrant such that dF = . b) The level curves of the function F (x, y) that you found in part a) are solutions to a first order differential equation. Write down that differential equation. 2 2. A tank contains 40 gallons of pure water. Starting at time zero, a saltwater solution containing 0.5 lb/gal of salt enters the tank at a rate of 2 gal/min. At the same time a drain is opened at the bottom of the tank allowing the saltwater solution to leave at a rate of 2 gal/min. Assume that the solution is kept perfectly mixed at all times. How long will it take for the amount of salt in the tank to reach 5 lbs? Leave your answer in exact form (in terms of logarithms). ...
View
Full
Document
This note was uploaded on 05/01/2008 for the course MATH 33B taught by Professor Staff during the Spring '07 term at UCLA.
 Spring '07
 staff
 Differential Equations, Equations

Click to edit the document details