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For the following problems, find the general solution to the differential equations.$$y^{\prime}=y \ln y$$

$y=\frac{x^{2} \ln (x)}{2}-\frac{x^{2}}{4}+C$

Calculus 2 / BC

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

Differential Equations

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Lectures

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For the following problems…

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So for these first up in this problem, I went ahead in rewrote ah Wai prime as D. Y T X And I did this because it's going to allow me to multiply both sides of my equation by the X and to start a separation of variables. So on the left side, we have d y. And on the right side, this is equal to Y d. X. So to finish separating our variables, I'm just going to divide both sides of the equation by why? And when I do that, I get one over. Why do you Why is equal to D X and from here? Because we have a separation of variables, we can go ahead and integrate each side of my equation independently. I'm so on the left side. We know that the integral of one over why is just the natural log of y and the integral of D X is going to be X and we'll write plus C on this side of the equation. And so finally we know that the natural log is telling us that why is equal to e to the X plus c power, Um and so we can go ahead and rewrite this in our final form of our general solution as wise equal to a E to the

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