Chapter 6.3, Problem 13E

### 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 5-18, find the general solution of the differential equation. y 2 y ′ = sin   9 x

To determine

To calculate: The general solution of the differential equation given as, y2y=sin9x.

Explanation

Given:

The differential equation is y2yâ€²=sin9x.

Formula used:

The differential equation is in the 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«xndx=xn+1n+1+C.

Calculation:

Consider the differential equation given as,

y2yâ€²=sin9x

Simplify,

y2dydx=sin9xy2dy=sin9xdx â€¦...â€¦... (1)

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

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