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MHT CET202016 Oct 2020Morning ShiftMathematicsDifferential EquationsActual

The differential equation obtained from the function y=a(x-a)² is

Options

  1. A8 y²= ( d y d x )² [x- 1 4 y ( d y d x )² ]²
  2. B8 y²= ( d y d x )² [x+ 1 4 y ( d y d x )² ]²
  3. C2 y²= ( d y d x )² [x- 1 4 y ( d y d x )² ]²
  4. D4 y²= ( d y d x )² [x- 1 4 y ( d y d x )² ]²

Correct answer

D. 4 y²= ( d y d x )² [x- 1 4 y ( d y d x )² ]²

Step-by-step solution

(B) aligned y &=a(x-a)²...(1) d y d x &=2 a(x-a)...(2) aligned Eq. (2)+ cq (1) gives ( d y d x ) y = 2 a(x-a) a(x-a)² (x-a)= 2 y ( d y d x ) and a=x- 2 y ( d y d x ) Substituting these values of a and (x-a) in eq. (1), we get aligned y &= [x- 2 y ( d y d x ) ] [ 2 y ( d y d x ) ]² &= [ x ( d y d x )-2 y ( d y d x ) ] [ 4 y² ( d y d x )² ] & (y) ( d y d x )³ x ( d y d x -2 y ) =4 y² aligned

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