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November 10th, 2011, 11:24 PM   #1
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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
ln|e^v-1|=ln|x^2|+c
Now i would simplify this to e^v-1=x^2+e^c but I am clearly doing something wrong because my tutor gets
ln|e^v-1|=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!
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November 11th, 2011, 02:19 AM   #2
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Re: Differential equation simplification





where is a constant
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November 12th, 2011, 07:25 PM   #3
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If y is defined for all real x,  where the constants A and B are non-negative.

I'll leave you to specify the domain if the constants are not both non-negative.
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