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Write the following first-order differential equations in standard form.$$-x y^{\prime}=(3 x+2) y+x e^{x}$$

$y^{\prime}+\frac{3 x+2}{x} y=-e^{x}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Missouri State University

Harvey Mudd College

Baylor University

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section four out 5 to 15 were asked to write this different equation in standard form. So keeping in mind standard form is gonna be why prime plus some function of X times Why is equal to some function of X? Okay, so in my case, if I take this equation, I can write this as negative x y prime plus it's with me minus three X plus two. Why is equal to X E to the minus X. Now I want this. Why Prime to be by itself, I could divide the entire equation by ex just would say negative X so I can Why Prime is equal to and this is gonna be minus three X plus two over minus X. Why is equal to minus E to the minus X and so I can simplify here than negatives were gonna go away. So this is sorry about this. This is a y Prime. Keep making this mistake right here. So you get it's gonna be a wide prime plus three x plus two over X. Why is it about a minus? E to the minus X

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