How do I integrate dy/dx = x - y please ?

dy/dx = x - y

Use
substitution:
v = x - y
Differentiate with respect to
x
dv/dx = 1 - dy/dx
dy/dx = 1 - dv/dx

Now we use
above substitutions in differential equations
dy/dx = x - y
1 -
dv/dx = v
dv/dx = 1 - v
dv/(1-v) = dx

Now
integrate both sides:

intg dv/(1-v) =
intg dx

-ln (1-v) =
x+c

 ln(1-v) = -x - c

1 - v =
e^(-x-c) = [e^(-x)][e^(-c)]

1 - v = (C)e^(-x)   ,  where C
= e^(-Cc)

1 - (x - y) =
(C)e^(-x)

y - x + 1 =
(C)e^(-x)

y = (C)e^(-x) + x -
1

Here is an example with a similar
problem.