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November 21st, 2011, 09:22 AM   #1
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differential equation

can anyone help me with this?:/
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November 21st, 2011, 09:50 AM   #2
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Re: differential equation





Integrate both sides.
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November 21st, 2011, 09:56 AM   #3
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Re: differential equation

Don't neglect the trivial solution y = k?, where k is an integer.
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November 21st, 2011, 10:20 AM   #4
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For y ? k?, let u = tan(y/2), then du/dx = (1/2)sec˛(y/2)dy/dx, so that dy/dx = 2(du/dx)/(1 + u˛).
Hence the equation becomes 2du/dx/(1 + u˛) = 2u/(1 + u˛), i.e., du/dx = u, which has solution u = Ce^x.
Therefore y = 2arctan(Ce^x) + 2k? or y = k? (as noted above), where C is a constant and k is an integer.
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November 21st, 2011, 12:10 PM   #5
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Re: differential equation

Quote:
Originally Posted by MarkFL
Don't neglect the trivial solution y = k?, where k is an integer.
y' = sin(y)
Cancelling y from both sides gives:
' = sin

Something seems fishy about my version of the trivial solution
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November 21st, 2011, 12:32 PM   #6
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Re: differential equation

and what about this?
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November 21st, 2011, 12:35 PM   #7
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Re: differential equation

Quote:
Originally Posted by BonTrust
and what about this?
Maybe a substitution can be useful ...
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November 21st, 2011, 12:49 PM   #8
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Re: differential equation

Well, that's the point... I'm very bad at math :/ I know to code web sites with html, css, jQuery, php, create programs in Java, knowing design patterns, uml and sql, but math is just too hard for me:/
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November 21st, 2011, 01:07 PM   #9
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Re: differential equation

We are given:



If we write it like this:



Observing we have the quotient rule on the left, we may then write:







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November 21st, 2011, 01:24 PM   #10
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Re: differential equation

Thanks it really helps to read some steps on how to do it
I have a question? Is this solution to other equation right? I was trying to do something by myself
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