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

Step-by-step solution

d y d x = x+y+1 x+y-1 Put x+y=t 1+ d y d x = d t d x array lc & d y d x = d t d x -1 & d t d x -1= t+1 t-1 & d t d x = t+1+t-1 t-1 & d t d x = 2 t t-1 & ( t-1 2 t ) d t=d x & ( 1 2 - 1 2 t ) d t=d x array On integrating, we get 1 2 t- 1 2 t=x+c₁ array lrl & t- t & =2 x+2 c₁ & x+y- (x+y) & =2 x+2 c₁ & y & =x+ (x+y)+c array