If a curve passes through the point 1 , - 2 and has slope of the tangent at any point x , y on it as x 2 - 2 y x , then the curve also passes through the point

Question

If a curve passes through the point 1 , - 2 and has slope of the tangent at any point x , y on it as x 2 - 2 y x , then the curve also passes through the point, 3 , 0, ( - 1 , 2 ), ( - 2 , 1 ), 3 , 0

MARKS App · Accepted Answer

d y d x = x 2 - 2 y x ⇒ d y d x + 2 x y = x . It is in linear form. I.F. = e ∫ 2 x d x = e 2 l n x = x 2 ∴ y . x 2 = ∫ x . x 2 d x = x 4 4 + c ∵ At x = 1 , y = - 2 , ∴ - 2 × 1 2 = 1 4 4 + c ⇒ c = - 2 - 1 4 = - 9 4 ∴ curve is y . x 2 = x 4 4 - 9 4 ∴ It passes through 3 , 0 .

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