   Chapter 6.2, Problem 12E

Chapter
Section
Textbook Problem

Solving a Differential Equation In Exercises 3-12, find the general solution of the differential equation. x y + y ' = 100 x

To determine

To calculate: The differential equation xy+y'=100x and finding a general solution.

Explanation

Formula used:

Integration of xn:

xndx=xn+1n+1+C

Integration of 1x:

1xdx=log|x|+C

Calculation:

Consider the given differential equation:

xy+y'=100x.

Rewriting above differential equation, we have:

xy+y'=100xy'=100xxydydx=x(100y)dy100y=xdx

Next, by integrating on both sides of the equation, we get:

dy100y=xdxln|100y|+C

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