Question

) dy 2x
------ = ---------------
dx yx2 + y

Answer 1

Explanation:

`(dy)/(dx) = (2x)/(y(x^2 + 1))`

Rearranging the terms, we get

`ydy = (2xdx)/(x^2 + 1)`

We then integrate the expression above to get

`\displaystyle \int ydy = \int (2xdx)/(x^2 + 1)`

`\displaystyle (1)/(2)y^2 = \ln |x^2 +1| + k`

or

`y = √(2\ln |x^2 + 1|) + k`

where I is the constant of integration.