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Chapter 2: Q38E (page 57)

Use the separation of variables technique to derive the solution (7) to the differential equation (6).

Short Answer

Expert verified

渭(x)=e鈭�P(x)dx

Step by step solution

01

Important formula

The required formula is鈭�xndx=xn+1n+1

02

Solve by variable separating

The differential equation of (6)渭'=渭pis

d渭dx=渭P(x)1渭d渭=鈭�P鈥�(x)鈥�dxln渭(x)=鈭�P鈥�(x)鈥�dx渭(x)=e鈭�P鈥�(x)鈥�dx+c
Therefore, this is the required equation (7)role="math" localid="1664162663857" 渭(x)=e鈭�P(x)dxwhere c is any constant.

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Most popular questions from this chapter

Use the method discussed under 鈥淗omogeneous Equations鈥� to solve problems 9 - 16.

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Question: In Problems 1-30, solve the equation.

dydx=2x+y-12

In problems 1 - 8 identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form Y'=G(ax+by).(y-4x-1)2dx-dy=0.

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