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MHT CET20225 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

General solution of the differential equation (y^3+y ) (x^2+1 ) d y= (x y^4+2 y^2 x ) d x is (where C is a constant of integration.)

Options

  1. Ay ^2 ( y ^2+1 )= C ( x ^2+1 )^2
  2. By ^2 ( y ^2+2 )= C ( x ^2+1 )
  3. Cy ^2 ( y ^2+2 )= C ( x ^2+1 )^2
  4. Dy^2 (y^2+1 )=C (x^2+2 )^2

Correct answer

C. y ^2 ( y ^2+2 )= C ( x ^2+1 )^2

Step-by-step solution

aligned & (y^3+y ) (x^2+1 ) d y= (x y^4+2 y^2 x ) d x & y^3+y y^4+2 y^2 d y= x x^2+1 d x & 1 4 _e (y^4+2 y^2 )= 1 2 _e (x^2+1 )+ C^1 & _e (y^4+2 y^2 )=2 _e (C^1 )^2 (x^2+1 ) & y^4+2 y^2= (c^1 )^4 (x^2+1 )^2 & y^2 (y^2+2 )=C (x^2+1 )^2 aligned

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