   Chapter 6, Problem 20RE

Chapter
Section
Textbook Problem

Solving a Differential Equation In Exercises 15–22, find the general solution of the differential equation. x y ' − ( x + 1 ) y = 0

To determine

To calculate: General solution of differential equation xy'(x+1)y=0.

Explanation

Given:

Differential equation: xy'(x+1)y=0

Formula used:

Integration of 1x is given by:

1xdx=lnx+C

According to property of logarithm

lnxlny=lnxy

Calculation:

Given equation can be written as

y'y=(x+1)x

Now integrate to both sides with dx

y'ydx=(x+1)xdx

And,

dyy=xxdx+1xdx

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