Differential equations

posted by Anonymous

(X+y) dx + xdy =0

  1. bobpursley

    (x+y)dx = -x dy

    -x dy /(x+y) dx = 1

    -x / [ x(1 +y/x)] dx = 1

    - dy /(1 +y/x) = dx

    Let u =y/x then xu = y so x du/dx + u = dy/dx.

    - (x du/dx + u) / ( 1+ u ) = 1

    x du/dx + u = -(1 + u)

    x du/dx + u = -1 - u

    x du/dx + 2u = -1

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

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

    x/dx = (-1 - 2u)/du

    du/(-1-2u) = dx/x

    (-1/2)log|-1 - 2u| = log|x| + C

    Multiplying by -2:

    log|-1-2u| = -2log|x| + C

    log|-1-2u| = log|1/x^2| + C

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