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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

If the general solution of the differential equation y ' = y x + ϕ x y , for some function ϕ , is given by yln | c x | = x , where c is an arbitrary constant, then ϕ 2 is equal to here , y ' = d y d x

Options

  1. A-4
  2. B- 1 4
  3. C1 4
  4. D4

Correct answer

B. - 1 4

Step-by-step solution

given : y ′ = y x + ϕ x y As y ln cx = x ⇒ y ′ ln cx + y 1 cx c = 1 ⇒ y ′ x y + y x = 1 ⇒ 1 - y x x y = y x + ϕ x y x = 2 , y = 1 ⇒ 1 - 1 2 2 1 = 1 2 + ϕ 2 1 ⇒ ϕ 2 = - 1 4

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