NDA2018MathematicsDifferential EquationsActual
What is the solution of the differential equation d x d y = x+y+1 x+y-1 ?
Options
- Ay-x+4 (x+y)=c
- By+x+c (x+y)=c
- Cy-x+ (x+y)=c
- Dy+x+2 (x+y)=c
Correct answer
C. y-x+ (x+y)=c
Step-by-step solution
Let t=x+y d t d y = d x d y +1 So, d t d y -1= t+1 t-1 aligned & d t d y = t+1+t-1 t-1 = 2 t t-1 & t-1 t d t=2 d y & t- t=2 y+ C ₁ & x+y- (x+y)-2 y= C ₁ & y-x+ (x+y)=- C ₁= C aligned