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Math Help - Verify a solution

  1. #1
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    Verify a solution

    Verify that xy=lny +c is a solution of the differential equation dy/dx=(y^2)/(1-xy) for every value of the constant c.

    I can't figure this one out...I don't even know where to start. Some help would be much appreciated. Thanks!
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  2. #2
    Member Black's Avatar
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    Use implicit differentiation on xy=\text{ln}y+c.
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  3. #3
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    Quote Originally Posted by ChingKing08 View Post
    Verify that xy=lny +c is a solution of the differential equation dy/dx=(y^2)/(1-xy) for every value of the constant c.

    I can't figure this one out...I don't even know where to start. Some help would be much appreciated. Thanks!
    we need to show that xy=lny +c satisfy DE dy/dx=(y^2)/(1-xy)

    start from xy=lny +c, differentiate it

    y + xy' = \frac{y'}{y}

    y(y + xy') = y'

    y^2 + xyy' = y'

    y^2 = y'(1 - xy)

    y' = \frac{y^2}{1-xy}

    so the equation xy=\ln y +c satisfy the differential equation dy/dx=(y^2)/(1-xy)
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