Calculus  Orthogonal Trajectories
posted by COFFEE .
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.
Yes, correct.
Yes, correct.
Thanks for checking!!!
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