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MHT CET202314 May 2023Morning ShiftMathematicsDifferential EquationsActual

The differential equation of y= e ^x( a x+ b x) is

Options

  1. Ad ^2 y ~d x^2 -2 d y ~d x -y=0
  2. Bd ^2 y ~d x^2 +2 d y ~d x +2 y=0
  3. Cd ^2 y ~d x^2 -2 d y ~d x +y=0
  4. Dd ^2 y ~d x^2 -2 d y ~d x +2 y=0

Correct answer

D. d ^2 y ~d x^2 -2 d y ~d x +2 y=0

Step-by-step solution

aligned & y= e ^x( a x+ b x) & d y ~d x = e ^x( a x+ b x) & + e ^x( ~b x- a x) & d y ~d x =y+ e ^x( ~b x- a x) & d ^2 y ~d x^2 = d y ~d x + e ^x( ~b x- a x) & + e ^x(- b x- a x) & d ^2 y ~d x^2 = d y ~d x + ( d y ~d x -y )-y & d ^2 y ~d x^2 -2 d y ~d x +2 y=0 & aligned

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