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December 5th, 2010, 03:22 PM  #1 
Member Joined: Oct 2010 Posts: 30 Thanks: 0  first order differential equations
Could someone help me with these questions, please? 1)Solve the following separable equation and verify your solution dy/dt+(e^y)=(e^y)sint 
December 5th, 2010, 03:28 PM  #2 
Member Joined: Jul 2009 From: New Jersey Posts: 65 Thanks: 0  Re: first order differential equations
How would you separate this equation?

December 5th, 2010, 03:33 PM  #3 
Member Joined: Oct 2010 Posts: 30 Thanks: 0  Re: first order differential equations
I have been trying to do it but can't figure out how; would you be able to work through it for me?

December 5th, 2010, 04:24 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: first order differential equations
You have: Subtract through by Factor right side: Multiply through by Integrate: To verify the answer, we can differentiate y with respect to t: 
December 6th, 2010, 09:20 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,310 Thanks: 1981 
y = ln(cos(t) + t + C), where t exceeds the root of cos(t) + t + C = 0, so that the logarithm is real.


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