Posted by COFFEE on Tuesday, June 26, 2007 at 1:17am.
Find the orthogonal trajectories of the family of curves:
y = k*(e^-x)
so k = y/(e^-x)
differentiating we get:
1 = -k(e^-x)*(dx/dy)
1/(dx/dy) = -k(e^-x)
dy/dx = -k(e^-x)...substituting for k:
dy/dx = -(y/(e^-x))*(e^-x)
dy/dx = -y
Integral(1/=y)dy = Integral dx
-ln(y) = x + C
x = -ln(y) + C
Is this correct? Thanks.
Thanks for checking!!!
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