   Chapter 6, Problem 38RE

Chapter
Section
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'eysinx=0

Formula used:

Integration of ex is given by:

enxdx=enxn+C

Integration of sinx is given by:

sinxdx=cosx+C

Calculation:

The given equation can be written as:

y'=eysinxy'ey=sinxy'ey=sinx

Integrate each side with respect to dx

eyy'dx=sinxdxeydy=sinxdx                         �

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