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

User Jedihawk
by
2.4k points

1 Answer

23 votes
23 votes

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.

User Chandan Rauniyar
by
3.0k points