Chapter 6.3, Problem 32E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

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

Finding a Particular Solution Curve InExercises 29-32, find an equation of the curve that passes through the point and has the given slope. ( 8 , 2 ) , y ' = 2 y 3 x

To determine

To calculate: The equation of curve that passes through the point (8,2) and has the slope y=2y3x.

Explanation

Given:

The point on the line (8,2) and the slope of the line is yâ€²=2y3x.

Formula used:

The differential equation in variable separable form, f(y)dy=g(x)dx where f(y)Â andÂ g(x) are the function in y and x respectively.

The integral formula is âˆ«1xdx=lnx+C where n is a constant value and x is a variable.

Calculation:

Consider the differential equation,

yâ€²=2y3x

It can also be represented as:

dydx=2y3xdyy=23â‹…dxx

This differential equation is of variable separable form, f(y)dy=f(x)dx

Now, integrate both the sides,

âˆ«dyy

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