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MHT CET20228 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

The differential equation whose solution is y=c^2+ c x , where c is constant, is

Options

  1. Ax^4 ( d y ~d x )^2-x d y ~d x -y=0
  2. Bx^2 ( d y ~d x )^2+ d y ~d x -y=0
  3. Cx ( d y ~d x )^2-x^2 d y ~d x +y=0
  4. Dx^4 ( d y ~d x )^2- d y ~d x +y=0

Correct answer

A. x^4 ( d y ~d x )^2-x d y ~d x -y=0

Step-by-step solution

aligned & y=c^2+ c x & d y ~d x = -c x^2 & c=-x^2 d y ~d x aligned aligned & Hence, y= (-x^2 d y ~d x )^2+ (-x^2 d y ~d x ) 1 x & y=x^4 ( d y ~d x )^2-x d y ~d x & x^4 ( d y ~d x )^2-x d y ~d x -y=0 aligned

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