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
- Ay=x (x+y)+c
- Bx-y= (x+y)+c
- Cx+y= (x+y)+c
- 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