If $ x d y=y d x+y^{2} d y $ and $ y(1)=1 $ then find the value of $ y(-3) $

Question

If $ x d y=y d x+y^{2} d y $ and $ y(1)=1 $ then find the value of $ y(-3) $,

MARKS App · Accepted Answer

Given that x d y = y d x + y 2 d y ∫ y d x - x d y y 2 = ∫ - d y We know that d x y = y d x - x d y y 2 x y = - y + c As, y 1 = 1 1 = - 1 + c ⇒ c = 2 ⇒ x y = - y + 2 If x = - 3 - 3 = - y 2 + 2 y ⇒ y 2 - 2 y - 3 = 0 ⇒ y = 3

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