classify the equation: (x)dy/dx + xy = 1-y linear, nonlinear, separable,exact, homogeneous, or one that requires an integration factor?

You need
to solve the exact differential equation, hence you should  divide by x both sides to preserve
the equation such that:

You need to
keep   to the left side, hence you need to subtract y both sides:

You need to
multiply by dx both sides such...