Question

Find the orthogonal trajectories of y=ce^(2x).

Answer 1

@SithsAndGiggles

Answer 2

I differentiated y=ce^(2x) with respect to x and got dy/dx=2ce^(2x). So the negative reciprocal of dy/dx=-1/(2ce^(2x)) and I need to solve for y from here.

Answer 3

Oh yeah, isn't it dy/dx=-1/2y?

Answer 4

Okay, so you have the separable equation,
\[\frac{dy}{dx}=-\frac{1}{2c}e^{-2x}\]
Given that \(y=ce^{2x}\), you have \(c=ye^{-2x}\), so yes, you get
\[\frac{dy}{dx}=-\frac{1}{2y}\]

Answer 5

I was thoughtless. See, I was stucked because I thought there's no y to replace it and substitute. Now I got it. Thanks for your time!