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
- A(1+ x)(1+ y)= c , where c is a constant of integration.
- B1+ x+ y= c , where c is a constant of integration.
- C(1+ x)(1+ y)= c , where c is a constant of integration.
- 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