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MHT CET202314 May 2023Morning ShiftMathematicsDifferential EquationsActual

General solution of the differential equation x(1+ y) d x- y(1+ x) d y=0 is

Options

  1. A(1+ x)(1+ y)= c , where c is a constant of integration.
  2. B1+ x+ y= c , where c is a constant of integration.
  3. C(1+ x)(1+ y)= c , where c is a constant of integration.
  4. D1+ x y= c , where c is a constant of integration.

Correct answer

C. (1+ x)(1+ y)= c , where c is a constant of integration.

Step-by-step solution

aligned & x(1+ y) d x- y(1+ x) d y=0 & x 1+ x ~d x- y 1+ y ~d y=0 aligned Integrating on both sides, we get aligned & |1+ x|+ |1+ y|= |c| & |(1+ x)(1+ y)|= |c| & (1+ x)(1+ y)=c aligned

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