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!!!
Answer this Question
More 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 ...
- mathematics - find orthogonal trajectory of family of circles x^2+y^2+2fy+1=0.
- 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...