Question

If (x + y) dx + (x – y) dy = 0, then
(a) x^2 + 2xy - y^2=C (b) x^2 - 2xy - y^2=C (c) x^2 + 2xy + y^2=C (d) x^2 - 2xy + y^2=C

Answer 1

is this an "exact" setup

Answer 2

if so ..... up the left, tack on a g(y), integrate it down to the dy stuff; and compare parts

Answer 3

int (x+y) dx to x^2/2 + xy + g(y)

derive wrt.y: x^2/2 + xy + g(y) to x + g'(y)

x-y = x+g'(y) tells us that g' = -y; therefore g= -y^2/2 + C

x^2/2 + xy - y^2/2 = C

scale it by 2 to unravel the options