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:

`dy/dx + y = (1-y)/x`

You need to
keep `dy/dx`  to the left side, hence you need to subtract y both sides:

`(dy)/dx = (1-y)/x - y =gt dy/dx = (1-y - xy)/x`

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