Question

dx-(x + y + 1)dy =0 , Solve the differential equations​

Answer 1

Answer:

x+y-1) dy=(x+y) dx

dyx+y=dxx+y−1=k say

Then k=dy+dxx+y+x+y−1=d(x+y)2(x+y)−1=12d(2x+2y−1)2x+2y−1

Also k=dy−dxx+y−x−y+1=d(y−x)1

So d(y−x)=12d(2x+2y−1)2x+2y−1

Integrating,

y−x=12ln|2x+2y−1|+C