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### Messages - Arash Jalili

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1
##### FE / Re: FE4
« on: December 10, 2014, 04:40:02 PM »
just realized I had a typo (missing a parenthesis):

v = y/x
=> y=vx => y' = v + v'x

xy' = y - xe^(y/x) => y' = y/x - e^(y/x)
=> v + v'x = v - e^v
=> v'x = -e^v
=> (-e^-v)dv = dx/x
=> e^(-v) = ln (x) + c
=> ln(e^-v) = ln(ln (x) +c)
=> v = -ln(ln(x) +c)
=> y = -xln(ln(x)+c)

y(1)=-2 => c = e^-2
=> y = -xln(ln(x) + e^-2)

2
##### FE / Re: FE4
« on: December 10, 2014, 12:26:57 PM »
I will take a chance since no one has responded. this could be very very wrong.

v = y/x
=> y=vx => y' = v + v'x

xy' = y - xe^(y/x) => y' = y/x - e^(y/x)
=> v + v'x = v - e^v
=> v'x = -e^v
=> (-e^-v)dv = dx/x
=> e^(-v) = ln x + c
=> ln(e^-v) = ln(ln x +c)
=> v = -ln(ln(x +c)
=> y = -xln(ln(x+c)

y(1)=-2 => c = e^-2
=> y = -xln(ln(x + e^-2)

Other than this I could think of using taylor series for the e^(y/x) to make it linear?

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