Chapter 6, Problem 38RE

### 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 General Solution Using Separation of Variables In Exercises 35–38, find the general solution of the differential equation. y ' − e y sin x = 0

To determine

To calculate: The general solution of differential equation y'eysinx=0.

Explanation

Given:

Differential equation: y'âˆ’eysinx=0

Formula used:

Integration of ex is given by:

âˆ«enxdx=enxn+C

Integration of sinx is given by:

âˆ«sinxdx=âˆ’cosx+C

Calculation:

The given equation can be written as:

y'=eysinxy'ey=sinxy'eâˆ’y=sinx

Integrate each side with respect to dx

âˆ«eâˆ’yy'dx=âˆ«sinxdxâˆ«eâˆ’ydy=âˆ«sinxdxÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ï¿½

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