Question

solve the differential equation (x+y-1)dy-(x+y)dx=0​

Answer 1

Answer:

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

dy/x+y=dx/x+y−1=k Then

k=dy+dx/x+y+x+y−1

=d(x+y)/2(x+y)−1

=1/2d(2x+2y−1)2x+2y−1

Also k=dy−dx/x+y−x−y+1

=d(y−x)/1

So d(y−x)=1/2d(2x+2y−1)/2x+2y−1

Integrating,

y−x=12ln|2x+2y−1|+C

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