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NDA2018MathematicsDifferential EquationsActual

What is the solution of (1+2 x) d y-(1-2 y) d x=0 ?

Options

  1. Ax-y-2 x y=c
  2. By-x-2 x y=c
  3. Cy+x-2 x y=c
  4. Dx+y+2 x y=c

Correct answer

A. x-y-2 x y=c

Step-by-step solution

aligned & (1+2 x) d y-(1-2 y) d x=0 (1+2 x) d y=(1-2 y) d x & d y 1-2 y = d x 1+2 x aligned Integrating both sides, d y 1-2 y = d x 1+2 x aligned & -1 2 (1-2 y )= 1 2 (1+2 x )+ 1 2 c & (1-2 y )+ (1+2 x )= c & (1+2 x )(1-2 y )= c & 1+2 x -2 y -4 xy = c & 2 x -2 y -4 xy = c & x - y -2 xy = c aligned

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