February 11th, 2012, 02:36 AM  #1 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Differentiation
After differentation dy/dx = x+y will become, to find the exact solution y = e^x  x  1 I need to do the same to dy/dx = y^3 (1x^2) Can anyone help? 
February 11th, 2012, 03:41 AM  #2 
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: Differentiation
The second ODE is separable. Finish it ... 
February 11th, 2012, 08:33 AM  #3 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Differentiation
Would it be 1/y=xx^3/3 
February 11th, 2012, 10:26 AM  #4 
Senior Member Joined: Dec 2011 From: Argentina Posts: 216 Thanks: 0  Re: Differentiation
For the first one you have Put the equation like this Multiply by Notice we don't exclude the 1 as an arbitrary constant since it is part of the particular solution to the equation. is the solution to the homogeneous equation. 
February 12th, 2012, 04:25 AM  #5 
Member Joined: Jan 2012 Posts: 82 Thanks: 0  Re: Differentiation
Thanks for that but I need a bit more help with the second

February 12th, 2012, 09:58 AM  #6 
Senior Member Joined: Dec 2011 From: Argentina Posts: 216 Thanks: 0  Re: Differentiation
For the second you separate variables, putting 
February 12th, 2012, 01:15 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,485 Thanks: 2041 
Or y = 0, which is the only real function that satisfies the equation for all real values of x.


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