Question

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

Answer 1

Step-by-step explanation:

$\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}$

Rearranging the terms, we get

$ydy = \dfrac{2xdx}{x^2 + 1}$

We then integrate the expression above to get

$\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}$

$\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k$

or

$y = \sqrt{2\ln |x^2 + 1|} + k$

where I is the constant of integration.