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MHT CET202310 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
  2. B1+ x+ y=c
  3. C(1+ x)(1+ y)=c
  4. D1+ x y=c

Correct answer

C. (1+ x)(1+ y)=c

Step-by-step solution

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

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