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JEE Main202124 Feb 2021Evening ShiftMathematicsDifferential EquationsActual

If a curve y = f x passes through the point 1 , 2 and satisfies x d y d x + y = b x 4 , then for what value of b , ∫ 1 2 f x d x = 62 5 ?

Options

  1. A31 5
  2. B10
  3. C5
  4. D62 5

Correct answer

B. 10

Step-by-step solution

d y d x + y x = b x 3 I . F . = e ∫ 1   x d x = x So, solution of D . E . is given by y · x = ∫ b · x 3 · x d x + c y = c x + b x 4 5 Passes through 1 ,   2 2 = c + b 5   … 1 ∫ 1 2 f x d x = 62 5 c   ln   x + b x 5 25 1 2 = 62 5 c   ln   2 + 31   b 25 = 62 5   … 2 By equation 1 and 2 c = 0 and b = 10

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