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Solve the differential equation.

$ y' + 2xy = 1 $

$$

y=\frac{\int e^{x^{2}} d x}{e^{x^{2}}}

$$

Differential Equations

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Missouri State University

Campbell University

University of Nottingham

Boston College

okay. We wanna solve this differential equation. So first, make sure why Prime is by itself. It is now find the integrating factor. And the integrating factor is e to the integral of what's ever in front of why two x dx. So that's each the X squared. So multiply everything by that. All right, I claim that this side is eat the X squared. Why? Quantity prime? Let's check and see. It's the first each the X squared times the derivative of the second. Why prime Plus the second Why times the derivative of the first, which is easy to the export times two x. All right now I'm gonna integrate both sides on this side. I get each the X squared y on this side. I get the inner girl, eat the X square DX plus c. Okay, that's not an integral that I know. In fact, it can't be integrated. Okay, you have to use some kind of trapezoid rule or something on it to integrate it. So divide each of the X squared on both sides and there is Thea answer to that one

Oklahoma State University

Differential Equations