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MHT CET202415 May 2024Morning ShiftMathematicsDifferential EquationsActual

The differential equation of y= e ^x ( a + b x+x^2 ) is

Options

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

Correct answer

C. d ^2 y ~d x^2 -2 ~d y ~d x -2 e ^x+y=0

Step-by-step solution

aligned & y= e ^x ( a + b x+x^2 ) & d y ~d x = e ^x ( a + b x+x^2 )+ e ^x( ~b +2 x) & d y ~d x =y+ e ^x( ~b +2 x) ...(i) & d ^2 y ~d x^2 = d y ~d x + e ^x( ~b +2 x)+ e ^x(2) & d ^2 y ~d x^2 = d y ~d x + d y ~d x -y+2 e ^x ...[From(i)] & ~d ^2 y ~d x^2 -2 ~d y ~d x -2 e ^x+y=0 aligned

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