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December 5th, 2010, 03:22 PM   #1
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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
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December 5th, 2010, 03:28 PM   #2
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Re: first order differential equations

How would you separate this equation?
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December 5th, 2010, 03:33 PM   #3
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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?
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December 5th, 2010, 04:24 PM   #4
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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:



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December 6th, 2010, 09:20 AM   #5
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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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