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November 21st, 2011, 09:22 AM  #1 
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  differential equation
can anyone help me with this?:/

November 21st, 2011, 09:50 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: differential equation Integrate both sides. 
November 21st, 2011, 09:56 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: differential equation
Don't neglect the trivial solution y = k?, where k is an integer.

November 21st, 2011, 10:20 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,020 Thanks: 2255 
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. 
November 21st, 2011, 12:10 PM  #5  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5  Re: differential equation Quote:
Cancelling y from both sides gives: ' = sin Something seems fishy about my version of the trivial solution  
November 21st, 2011, 12:32 PM  #6 
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  Re: differential equation
and what about this?

November 21st, 2011, 12:35 PM  #7  
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: differential equation Quote:
 
November 21st, 2011, 12:49 PM  #8 
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  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:/

November 21st, 2011, 01:07 PM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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: 
November 21st, 2011, 01:24 PM  #10 
Newbie Joined: Oct 2011 Posts: 17 Thanks: 0  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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