Question

y(1+y).dx + x(1-xy).dy=0​

Answer 1

Answer:

The given differential equation is

(1 + xy)ydx + x(1 – xy)dy = 0

ydx + xdy + xy(ydx – xdy) = 0

d(xy) + xy(ydx – xdy) = 0

(d(xy)/(xy)) + (ydx – xdy) = 0

d(xy)/(xy) = (xdy – ydx)

d(xy)/(xy)2 = (xdy – ydx)/xy = (dy/y) – (dx/x)

Integrating, we get

– (1/xy) = log |(y/x)| + c

which is the required solution