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Find the orthogonal trajectories of the family of curves. Sketch several members of each family.$$y=c x^{2}$$

Calculus 2 / BC

Chapter 16

First-Order Differential Equations

Section 3

Applications

Differential Equations

Campbell University

Idaho State University

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:48

Find the orthogonal trajec…

01:26

02:57

Find the equation of the o…

08:24

Determine the orthogonal t…

09:36

03:14

03:35

03:04

01:08

in this video, we're gonna go to the Ansett's question about six, which have a 16.3 to ratify the orthogonal trajectories to the family of curves and my wise you want to see X squared? Let's find the brilliant off this from your curves. So just differentiating there's gonna be to see of X so that for uh oh, I thought, you know, trajectories are gonna have Grady. And given by the Y, the X is equal to negative is typical of this so we can integrate that. Ah, see, we can interpret that using separation variables Philippines great left inside like so I would take a a constant minus 1/2. I wanted to see as integral one of acts the X And let's add to that a constant of integration was Call it G integration Left inside, we get why that's equal to minus one over to see integrate one over X and you get the natural log of X. That's like the great Innovex. Sorry, the National Ogilvy Absolute value of X plus day as that's the, uh, all the books directories

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