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MHT CET202120 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation d y d x = x+y+1 x+y-1 is given by

Options

  1. Ay=x (x+y)+c
  2. Bx-y= (x+y)+c
  3. Cx+y= (x+y)+c
  4. Dy=x+ (x+y)+c

Correct answer

D. y=x+ (x+y)+c

Step-by-step solution

d y d x = x+y+1 x+y-1 Put x+y=u 1+ d y d x = d u d x aligned & du dx -1= u +1 u -1 du dx = du +1 dx -1 +1= 2 u u -1 & ( u -1 u ) du =2 dx aligned Integrating both sides, we get aligned & d u- d u u = 2 d x & u- u=2 x+c & x+y- (x+y)=2 x+c y=x+ (x+y)+c aligned

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