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Question: Answered & Verified by Expert

If the general solution of the differential equation y'=yx+ϕxy, for some function ϕ , is given by yln|cx|=x, where c is an arbitrary constant, then ϕ2 is equal to here, y'=dydx

MathematicsDifferential EquationsJEE Main
Options:
  • A -4
  • B - 1 4
  • C 1 4
  • D 4
Solution:
2189 Upvotes Verified Answer
The correct answer is: - 1 4
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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