Chapter 6, Problem 39RE

### 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 Using Separation of Variables In Exercises 39-42, find the particular solution of the differential equation that satisfies the initial condition.Differential Equation Initial Condition y 3 y ' − 3 x = 0 y ( 2 ) = 2

To determine

To calculate: Particular solution of differential equation y3y'3x=0 for y(2)=2.

Explanation

Given:

Differential equation y3y'âˆ’3x=0

And,

y(2)=2

Formula used:

Integration of xn is given by

âˆ«xndx=xn+1n+1+C

Calculation:

The given differential equation can be written as y3y'=3x

Integrate each side with respect to x

âˆ«y3y'dx=âˆ«3xdxâˆ«y3dy=âˆ«3xdxÂ Â Â Â Â Â Â Â

Thus,

y3+13+1+C1=3x1+1

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