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NDA2017MathematicsDifferential EquationsActual

What is the general solution of the differential equation y d x- (x+2 y^2 ) d y=0 ?

Options

  1. Ax=y^2+c y
  2. Bx =2 cy ^2
  3. Cx=2 y^2+c y
  4. DNone of the above

Correct answer

C. x=2 y^2+c y

Step-by-step solution

aligned & y d x- (x+2 y^2 ) d y=0 & y d x-x d y-2 y^2 d y=0 & y-x d y d x =2 y^2 d y d x & y-x d y d x y^2 =2 d y d x aligned Integrating aligned & x y =2 y+c & x=2 y^2+c y aligned

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