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A solution of the differential equation ( d y d x )^2-x d y d x =0 is

Options

  1. Ay=2 x
  2. By=2 x+4
  3. Cy=x^2-1
  4. Dy= (x^2-2 ) 2

Correct answer

D. y= (x^2-2 ) 2

Step-by-step solution

( d y d x )^2-x ( d y d x )=0 d y d x [ d y d x - ]= d y d x =0 or d y d x =x New d y=x d x d y= x d xy= x^2 2 +C y= x^2+2 C 2 y= x^2 2 +C y= x^2+2 C 2 Comparing with options, y= x^2-2 2

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