My background knowledge
This picture is ideal OP-AMP:
where $$Vo=A(V_+ - V_-)...(0)$$
When I configure the non-inverting amplifier mode:
$$(V_i-V_o\frac{R_1}{R_f+R_1})A = V_o....(1)$$
$$V_iA=V_o+(\frac{R_1}{R_f+R_1})V_oA=V_o(1+A\frac{R_1}{R_f+R_1})....(2)$$
$$\frac{V_o}{V_i}=\frac{A}{1+A\frac{R_1}{R_1+R_f}}=\frac{1}{\frac{1}{A}+\frac{R_1}{R_1+R_f}}....(3)$$
when
$$A>>\infty$$ (ideal OP-AMP)
then
$$\frac{V_o}{V_i}=\frac{1}{\frac{R_1}{R_1+R_f}}=\frac{R_1+R_f}{R_1}=1+\frac{R_f}{R_1}$$
$$\frac{V_o}{V_i}$$
would converge to
$$1+\frac{R_f}{R_1}$$ (constant)
when I configure OP-AMP as negative feedback
So there is stable.
My question
If I configure OP-AMP as positive feedback with same circuit and same OP-AMP model
To calculate Vo/Vi,
I just swap $$Vi$$ and $$V_o\frac{R_1}{R_f+R_1}$$ from the equation (1)
Because this equation
$$Vo=A(V_+ - V_-)...(0)$$
is the same whether I configure OP-AMP as positive feedback or negative feedback.
So:
$$(V_o\frac{R_1}{R_f+R_1}-V_i)A = V_o....(4)$$
$$V_iA=(\frac{R_1}{R_f+R_1})V_oA-V_o=V_o(A\frac{R_1}{R_f+R_1}-1)....(5)$$
$$\frac{V_o}{V_i}=\frac{A}{A\frac{R_1}{R_1+R_f}-1}=\frac{1}{\frac{R_1}{R_1+R_f}-\frac{1}{A}}....(6)$$
If
$$A>>\infty$$ (ideal OP-AMP)
then
$$\frac{V_o}{V_i}=1+\frac{R_f}{R_1}$$
Above equation is the same to the result of negative feedback.
-- The constant result
Should positive configuration be oscillation??
Why does I get the constant gain?
So when I configure OP-AMP as positive feedback,
it's stable and linear operation same to negative feedback?