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MHT CET202416 May 2024Evening ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation d y ~d x =y x-y^2 x is

Options

  1. Ax=( c + x) y , where c is constant of integration.
  2. By=( c + y) x , where c is constant of integration.
  3. Cx=( c + x) y , where c is constant of integration.
  4. Dy=( c + y) , where c is constant of integration.

Correct answer

C. x=( c + x) y , where c is constant of integration.

Step-by-step solution

aligned & d y ~d x =y x-y^2 x & 1 y^2 ~d y ~d x + x (- 1 y )=- x (i) & Put v =- 1 y dv ~d x = 1 y^2 ~d y ~d x aligned dv d x +( x) v =- x [ From (i) ] I.F. = e ^ x dx = e ^ ( x) = x solution of the given equation is aligned & v. x= - x x ~d x+ c ₁ & v x=- x+ c ₁ & - 1 y x=- x+ c ₁ & x=y( x+ c ), where c =- c ₁ aligned

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