Final answer to the problem
$y=2+\frac{C_0}{\sqrt{\left(x^2+1\right)^{3}}}$
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1
Divide all the terms of the differential equation by $x^2+1$
$\frac{x^2+1}{x^2+1}\frac{dy}{dx}+\frac{3xy}{x^2+1}=\frac{6x}{x^2+1}$
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$\frac{x^2+1}{x^2+1}\frac{dy}{dx}+\frac{3xy}{x^2+1}=\frac{6x}{x^2+1}$
Learn how to solve problems step by step online. (x^2+1)dy/dx+3xy=6x. Divide all the terms of the differential equation by x^2+1. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{3x}{x^2+1} and Q(x)=\frac{6x}{x^2+1}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Final answer to the problem
$y=2+\frac{C_0}{\sqrt{\left(x^2+1\right)^{3}}}$
