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November 21st, 2011, 02:29 PM  #11 
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  Re: differential equation
I know I'm asking for much, but this is the last one I'm asking you guys to help me with 
November 21st, 2011, 02:31 PM  #12 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: differential equation
For the one you uploaded the image of your working: We are given: Separate variables: Convert from exponential to logarithmic form: 
November 21st, 2011, 05:52 PM  #13  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: differential equation Quote:
Divide through by : Separate variables: The solution can then be given implicitly by:  
November 21st, 2011, 10:46 PM  #14  
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  Re: differential equation Quote:
 
November 21st, 2011, 10:55 PM  #15 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: differential equation
Sometimes, you get an implicit relationship between the dependent and independent variables, rather than an explicit one. With this one, we could solve for x, to get x as a function of y...

November 22nd, 2011, 03:43 AM  #16 
Global Moderator Joined: Dec 2006 Posts: 21,128 Thanks: 2337 
There was nothing in the original equation to suggest that y was the dependent variable and x the independent variable.


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