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November 11th, 2011, 12:24 AM  #1 
Newbie Joined: Nov 2011 Posts: 4 Thanks: 0  Differential equation simplification
Hi. Just need some help understanding how my tutor simplified a differential equation and what laws he used to get his answer. The question is: e^(y/x)y'=2(e^(y/x)1)+(y/x)e^(y/x)  use the substitution y=xv(x) to solve this. I can post my whole working if you need to see it but basically both mine and the tutors answers simplify to this point lne^v1=lnx^2+c Now i would simplify this to e^v1=x^2+e^c but I am clearly doing something wrong because my tutor gets lne^v1=x^2*e^c which then somehow simplifies to cx^2 some basic law seems to be hovering just out of reach. Would appreciate an explanation. Thanks! 
November 11th, 2011, 03:19 AM  #2 
Newbie Joined: Oct 2011 Posts: 26 Thanks: 0  Re: Differential equation simplification where is a constant 
November 12th, 2011, 08:25 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 21,105 Thanks: 2324 
If y is defined for all real x, where the constants A and B are nonnegative. I'll leave you to specify the domain if the constants are not both nonnegative. 

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differential, equation, simplification 
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