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MHT CET20244 May 2024Evening ShiftMathematicsDifferential EquationsActual

The differential equation obtained by eliminating arbitrary constant from the equation y^2=(x+c)^3 is

Options

  1. A( d y ~d x )^3=27 y
  2. B( d y ~d x )^3=-27 y
  3. C8 ( ~d y ~d x )^3=27 y
  4. D8 ( ~d y ~d x )^3+27 y=0

Correct answer

C. 8 ( ~d y ~d x )^3=27 y

Step-by-step solution

y^2=(x+c)^3 Differentiating w.r.to x , we get aligned & 2 y ~d y ~d x =3(x+ c )^2 & (x+ c )^2= 2 y 3 ~d y ~d x & (x+ c )^6= ( 2 y 3 ~d y ~d x )^3 & ((x+ c )^3 )^2= 8 y^3 27 ( ~d y ~d x )^3 & (y^2 )^2= 8 y^3 27 ( ~d y ~d x )^3 & y^4= 8 y^3 27 ( ~d y ~d x )^3 & 27 y=8 ( ~d y ~d x )^3 aligned

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