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

Question

) dy 2x
—— = —————
dx yx2 + y

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Thanh Hà 1 month 2021-08-03T04:42:51+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-03T04:44:46+00:00

    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.

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