MHT CET202410 May 2024Morning ShiftMathematicsDifferential EquationsActual
The general solution of d y ~d x = x+y+1 x+y-1 is
Options
- Ay=x+ (x+y)+ c , where c is a constant of integration.
- By=x- (x+y)+ c , where c is a constant of integration.
- Cy=x- (2 x+y)+ c , where c is a constant of integration.
- Dy=x^2+ (x+y)+ c , where c is a constant of integration.
Correct answer
A. y=x+ (x+y)+ c , where c is a constant of integration.
Step-by-step solution
d y ~d x = x+y+1 x+y-1 ...(i) Put x+y= v ...(ii) d y ~d x = dv ~d x -1...(iii) Substituting (ii) and (iii) in (i), we get aligned & d v d x -1= v+1 v-1 & d v d x = 2 v v-1 v-1 2 v d v=d x aligned Integrating on both sides, we get aligned & v 2 - 1 2 v =x+ c ₁ & v - v =2 x+2 c ₁ & x+y- (x+y)=2 x+2 c ₁ & y=x+ (x+y)+ c , where c =2 c ₁ aligned