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What are the integrating factors for the following differential equations?$$y^{\prime}=x y+3$$

$\mu(x)=e^{-\frac{x^{2}}{2}}$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

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Hi. In this question, we are asked to find an integrating factor for this equation. Why prime equal X Y plus three. First thing in fighting integrating factor. You want to arrange your equation into the standard form that we use every time Here we do this to five p of X, and in this case it is minus X. When we help this, then we how if I'm alive for integrating factor as your ex equals e the constant e power to the p of it in the goal p m X dx Here it is usually a function. So it's constant e power by this function. And let's do this we integrate minus x the X and thing is just normal polynomial we would have yeah, minus X squared over two. Here. You usually have this constant term when we do indefinite in the call, right, But in this case, we can only them be careful just just for this integrating factor in this step that we can omit them in other other step, like usually solving, solving or the e u cannot omit this. Just be careful. Yeah, And that is it. In this question, we have integrating factor as sorry. We need to power. Even though this isn't it, so is E two D minus X squared over two. This is our integrating factor. Thank you.

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