Determine if the given differential equation is exact. If it is exact solve it.

Question

Answer 1

(3/x - 1 - y)dx + (3/y - 1 - x)dy = 0

∂/∂y(3/x - 1 - y) = - 1 = ∂/∂x(3/y - 1 - x) = -1. So this is exact equation.∂

∂F(x,y)/∂x = 3/x - 1 - y; F(x,y) = ∫(3/x - 1 - y)dx = 3lnx - x - yx + f(y);

∂F(x,y)/∂y = - x + f'(y) = 3/y - 1 - x; f'(y) = 3/y - 1; f(y) = 3lny - y + C;

F(x,y) = 3lnx - x - yx + 3lny - y = C is general solution for this equation.