Celulares

place

u = x/y

u' = (y - xy')/y^2 = xu(1-uy') = xu - y'xu^2

y' = (xu-u')/(xu^2)

So your ODE becomes

(xu-u')/(xu^2) = u + 1/u +1

xu - u' = xu^3 + xu + xu^2

u' = -xu^2(1+u)

u'/{u^2(1+u)} = -x

Now you have your variables seperated

[1/(1+u) - (u-1)/u^2 ] du = -x dx

ln(1+u) - ln u - u^(-1) + ln C = - x^2

ln[C(1+u)/u] = -x^2 + 1/u

C(1+u)/u = e^(1/u)/e^(x^2)

u/(1+u) * e^(1/u) = C * e^(x^2)

x/(x+y) * e^(y/x) = C * e^(x^2).... edit finished

“... mathematics is only the art of saying the same thing in different words” - B. Russell

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06-26-2007, 10:15 PM #4

stapel

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