   Chapter 6, Problem 22RE

Chapter
Section
Textbook Problem

Solving a Differential Equation In Exercises 15–22, find the general solution of the differential equation. y ' + x y = 9 x

To determine

To calculate: General solution of differential equation y'+xy=9x.

Explanation

Given:

Differential equation: y'+xy=9x

Formula used:

xndx=xn+1n+1+c

Calculation:

Given equation can be written as

y'=9xxyy'=x(9y)y'9y=x

Now integrate to both sides with dx

y'9ydx=xdxy'y9dx=xdxdyy9=xdx …...…... (Asdy=y'dx) (1)

Let z=y9

By differential both side

dz=dy

Now put values of z and dz in equation (1):

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