Differential equations
posted by Anonymous
(X+y) dx + xdy =0

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/(12u) = dx/x
(1/2)log1  2u = logx + C
Multiplying by 2:
log12u = 2logx + C
log12u = log1/x^2 + C
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