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MHT CET20239 May 2023Evening ShiftMathematicsDifferential EquationsActual

If f ^ (x)=x- 5 x^5 and f (1)=4 , then f (x) is

Options

  1. Ax^2 2 + 9 4 1 x^4 + 5 4
  2. Bx^2 2 - 5 4 1 x^4 + 9 4
  3. Cx^2 2 + 5 4 1 x^4 + 9 4
  4. Dx^2 2 - 9 4 1 x^4 + 5 4

Correct answer

C. x^2 2 + 5 4 1 x^4 + 9 4

Step-by-step solution

Given f ^ (x)=x- 5 x^5 Integrating both sides, we get array ll & f (x)= (x- 5 x^5 ) d x & f (x)= x^2 2 + 5 4 1 x^4 + c & But f (1)=4 & 1 2 + 5 4 + c =4 & c = 9 4 & f (x)= x^2 2 + 5 4 1 x^4 + 9 4 array

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