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.

Yes, correct.

Yes, correct.

Thanks for checking!!!

## Answer this Question

## Related Questions

- calculus - two curves are orthogonal at a point of intersection of their ...
- Math - Mark each of the following True or False. ___ a. All vectors in an ...
- Calculus - Find the orthoganal trajectories of the family. Use a graphing ...
- Math - I'm doing a bunch of practice finals and I don't know how to approach ...
- Math - Vectors - Prove that vector i,j and k are mutually orthogonal using the ...
- Linear Algebra, orthogonal - The vector v lies in the subspace of R^3 and is ...
- calculus - if the tangent of two intersecting circles, at their points of ...
- Calculus - What is the orthogonal trajectory of y^2 - x^2 = C ??
- calculus - Find an equation of the plane orthogonal to the line (x,y,z)=(-4,-9,9...
- Calculus-PLZ help! - Given u=3i-2j+k,v=2i-4j-3k, w=-i+2j+2k, 1 Find a unit ...