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Differential Equations #3

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Scholar
Karma Points: 203
Respect (98%):
Date Posted: 7/11/2008 11:15:22 AM  Status: Live
Differential Equations #3
Course Textbook Chapter Problem
N/A N/A N/A N/A
Question Details:
a).Show that each member of the one parameter family of functions is a solution of the differential equation
 
b). Find the solution of the inital value problem ; y(1)=-1
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Oracle
Karma Points: 9,222
Date Posted: 7/12/2008 1:06:48 PM  Status: Live
Asker's Rating: Lifesaver   
Response:
 
 
===> 
 
plug into the expression of the DE
 
thus: 
 
 
this is exactly what you want to prove
 
therefore: each member of the one parameter ( the parameter here is C ) family of functions is a solution of the differential equation
 
b)
 
when x = 1 ====> y(1) = -1  ====>   
 
====> C.e + 1 = -1   ====>   C = -2/e
 
thus the solution is :
 
hope this helps
 
 
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