The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant)

Question

The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant), x 2 y + y + c = 0, x 2 y + c y + 1 = 0, x y + y + c = 0, x y 2 + c y + y = 0

MARKS App · Accepted Answer

Given, d y d x = 2 y 2 x ⇒ ∫ d y y 2 = ∫ 2 x d x or - 1 y = x 2 + c or x 2 y + c y + 1 = 0

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