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For the following problems, draw the directional field associated with the differential equation, then solve the differential equation. Draw a sample solution on the directional field.$$y^{\prime}=\frac{1}{x}+\ln x-y, \text { for } x > 0$$

$y(x)=\ln x+C e^{-x}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Campbell University

Harvey Mudd College

University of Nottingham

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Draw the direction field f…

So they tell us that y zero equals one, which means we're gonna be laying down here and now our slope graph looks like this. So basically means that it's gonna look like flat here, and then it's gonna go for it. So this is basically the shape and then you're bounded by you're bounded by, um, excuse or why zero and why? Because, too

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