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JEE Main2015MathematicsDifferential EquationsActual

The solution of the differential equation y d x - x + 2 y 2 d y = 0 is x = f y . If f - 1 = 1 , then f ( 1 ) is equal to

Options

A2
B3
C4
D1

Correct answer

B. 3

Step-by-step solution

y d x - x d y = 2 y 2 d y y d x - x d y y 2 = 2 d y d x y = 2 d y ∫ d x y = 2 ∫ d y x y = 2 y + c x = 2 y 2 + c y If y =   - 1 ,   x = 1 1 = 2 - c c = 1 ∴ Curve would be x = 2 y 2 + y If y = 1 then x = 3   .

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