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Chapter 6.3, Problem 48E
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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding Orthogonal Trajectories In Exercises 43-48, find the orthogonal trajectories of the family. Use a graphing utility to graph several member, of each family. y = C e x

To determine

To calculate: The orthogonal trajectory of the family of curve y=Cex and use graphing utility to graph the family of curve.

Explanation

Given:

The provided family of curve is y=Cex.

Calculation:

Let us consider the given equation y=Cex â€¦â€¦ (1)

Now, differentiate equation (1) with respect to x and get the differential equation,

dydx=Cex â€¦â€¦ (2)

Now put value of Cex in equation (2),

dydx=y

As we know that dydx represents the slope of the given family of curves at (x,y), it follows that the orthogonal family has negative reciprocal slope, that is âˆ’1y .

So,

dydx=âˆ’1y

This gives,

ydy=âˆ’dx

This differential equation is of variable separable form,

f(y)dy=g(x)dx

Now, integrate to get,

âˆ«ydy=âˆ«âˆ’dxy22=âˆ’x+c1y2=âˆ’2x+2c1y2+2x=c

Here,2c1=c

Thus, the family of orthogonal trajectories is y2+2x=c

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