Step-by-step explanation:
[tex]\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}[/tex]
Rearranging the terms, we get
[tex]ydy = \dfrac{2xdx}{x^2 + 1}[/tex]
We then integrate the expression above to get
[tex]\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}[/tex]
[tex]\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k[/tex]
or
[tex]y = \sqrt{2\ln |x^2 + 1|} + k[/tex]
where I is the constant of integration.
