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Solve the differential equation.

$ xy' + y = \sqrt x $

$$y=\frac{2}{3} \sqrt{x}+C / x$$

Differential Equations

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Missouri State University

Baylor University

University of Nottingham

Yeah. Okay. If I ask you what's the derivative of X. Y. You would say X. This is with respect to X. X times the derivative of Y plus Y times the derivative of X. Which is what we have here. So this site turns into X. Y. Prime and this side turns into the square root of X. Okay, so now what I'm gonna do is if I have the derivative here now I'm going to integrate. Okay, so want to integrate. So the integral of the derivative is the stuff. And this gives you X to the three halves over three halves plus C, divide everything by X. And you get Y equals two thirds next to the one half plus C over X. And that is the solution to this differential equation.

Oklahoma State University

Differential Equations