Homework-4-s12-SOLUTION

Homework-4-s12-SOLUTION - 1 AMS 361: Applied Calculus IV...

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Unformatted text preview: 1 AMS 361: Applied Calculus IV (DE & BVP) Homework 4 Assignment Date: Wednesday (02/08/2012) Collection Date: Wednesday (03/07/2012) Grade: Each problem is worth 10 points Problem 4.1: Solve the following DE using two methods considered in Chapter 1: 1 + 2 ! = 1 + ! Solution : Method I: exact equation method: 1 + 2 = 1 + ! 1 + ! 1 + 2 = So = 1 + ! , = ( 1 + 2 ) ! = 2 , ! = 2 , ! ! = 4 1 + ! = ! ! ! ! ! ! ! !" = ( 1 + ! ) ! ! Then we will get = = 1 + ! ! ! = = 1 + 2 1 + ! ! ! From the first equation, we get = 1 + ! ! ! = 1 + ! ! ! + ( ) Substituting the above to the second equation, we get = 1 + ! ! ! + = 2 1 + ! ! ! + ! = ( 1 + 2 ) ( 1 + ! ) ! ! So ! = ( 1 + ! ) ! ! 2 = ( 1 + ! ) ! ! = 1 2 1 + ! + + ! = 1 + ! ! ! 1 2 1 + ! + + ! The general solution is 1 + ! 1 2 1 + ! + = Method II: Regarding x and y as dependent and independent variables respectively, 1 + 2 = 1 + ! 1 + 2 = ( 1 + ! ) ! 2 1 + ! = 1 1 + ! This is a linear first order DE in terms of x = 2 1 + !...
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This note was uploaded on 03/22/2012 for the course AMS 361 taught by Professor Staff during the Spring '08 term at SUNY Stony Brook.

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Homework-4-s12-SOLUTION - 1 AMS 361: Applied Calculus IV...

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