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MHT CET20249 May 2024Morning ShiftMathematicsDifferential EquationsActual

The curve satisfying the differential equation y ~d x- (x+3 y^2 ) dy =0 and passing through the point (1,1) also passes through the point

Options

  1. A( 1 4 , 1 2 )
  2. B( 1 4 ,- 1 2 )
  3. C( 1 3 ,- 1 3 )
  4. D(- 1 3 , 1 3 )

Correct answer

D. (- 1 3 , 1 3 )

Step-by-step solution

aligned & y ~d x- (x+3 y^2 ) d y=0 & y ~d x= (x+3 y^2 ) d y & ~d x ~d y = x+3 y^2 y & ~d x ~d y = x y +3 y & ~d x ~d y - ( 1 y ) x=3 y aligned Which is a linear equation IF = e ^ -1 y ~d y = e ^ - y = 1 y The required solution is x 1 y = 3 y 1 y ~d y+ c aligned & x y =3 y+c & x=3 y^2+c y aligned Curve passes through (1,1) aligned & 1=3+c & c=-2 aligned Equation (i) becomes, x=3 y^2-2 y Option (D) i.e., ( -1 3 , 1 3 ) Satisfies above equation.

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