   Chapter 6.3, Problem 14E

Chapter
Section
Textbook Problem

Finding a General Solution Using Separation of Variables In Exercises 5-18, find the general solution of the differential equation. y y ′ = − 8   cos ( π x )

To determine

To calculate: The general solution of the differential equation given as, yy=8cosπx.

Explanation

Given:

The differential equation is yy=8cosπx.

Formula used:

The differential equation is in the variable separable form, f(y)dy=g(x)dx where f(y) and g(x) are the functions of y and x respectively.

The integral formula is xndx=xn+1n+1+C.

Calculation:

Consider the differential equation given as,

yy=8cosπx

This implies,

ydydx=8cos(πx)ydy=8cos(πx)dx

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

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