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NDA2022MathematicsDifferential EquationsActual

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

Options

  1. Ay= ( x 2 )-x+c
  2. By= 1 2 ( x 2 )-x+c
  3. Cy=2 ( x 2 )-x+c
  4. Dy= ( x 2 )-2 x+c

Correct answer

C. y=2 ( x 2 )-x+c

Step-by-step solution

aligned & (d y-d x)+ x(d y+d x)=0 & (1+ x) d y=(1- x) d x & d y d x = 1- x 1+ x = ^2 x 2 = ^2 x 2 -1 & d y= ( ^2 x 2 -1 ) d x & y=2 x 2 -x+C aligned

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