Calculus - Orthogonal Trajectories

posted by .

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!!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Vectors

    Prove that vector i,j and k are mutually orthogonal using the dot product. What is actually meant by mutually orthogonal?
  2. Linear Algebra, orthogonal

    The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 …
  3. Math

    Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. …
  4. calculus

    two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and …
  5. Calculus

    Find the orthoganal trajectories of the family. Use a graphing utility to graph several members of each family. y = Ce^x What am I supposed to do here?
  6. Math

    I'm doing a bunch of practice finals and I don't know how to approach this problem. Find a vector a such that a is orthogonal to < 1, 5, 2 > and has length equal to 6. If I want to find a vector that is orthogonal to <1,5,2>, …
  7. mathematics

    find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.
  8. calc 2

    Find the orthogonal trajectories for the family of curves y=(kx)^6.
  9. math

    Find the orthogonal trajectories of family of the circle x2+y2=a2 where a is a parameter
  10. Math

    Find the orthogonal trajectory of the family of circle x^2 (y-c)^2 c^2 where c is parameter.

More Similar Questions