Question

(y+xy)dx +(x-xy^2)dy=0

Answer 1

(y+xy)dx + (x-xy^2)dy = 0

(y+xy)dx = -(x-xy^2)dy

y (1+x)dx = -x(1-y^2)dy

integral ((1+x)/x )dx = -integral ((1-y^2)/y)dx

Int (1/x dx) +int (x/x dx) = -int (1/y dy) + int (y^2/y^2) dy

log (x) + x = -log (y) + y^2/2 + C

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

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

(°_^)