Complete expression for current induced in a conductive loop

What is the complete general expression for the electric current $i$ induced in a coreless conductive loop of inductance $L$ and resistance $R$ when it is subjected to a given external magnetic flux, which is varying linearly from zero to some $Phi_{EXT}$ in time interval $t_1-t_0$. Assume $i(t_0)=0$

According to the Lenz Law, the current induced in the loop generates a counter-flux $Phi_L$ that opposes the external flux $Phi_{EXT}$ , which attempts to thread the loop.

The Net flux through the loop is equal to the sum of the external flux attempting to thread the loop and the counter-flux due to the induced current $Phi_{NET} = Phi_{EXT}+Phi_L$.

When the resistance of the loop is zero then the opposition of the counter-flux to the external flux is complete ( $Phi_L=-Phi_{EXT}$ ) and $Phi_{NET}$ remains constant perpetually.

The expression for the induced current must reduce to $i(t)=0$ when R is infinite.
Also, this expression must reduce to $i(t)=frac{Phi_L(t)}{L}$ or to $i(t)=frac{-Phi_{EXT}(t)}{L}$ when R is zero (see this answer).

Obviously, the expression:

$$i(t)=-frac{d Phi_{EXT}}{d t}/R$$

…does not fulfill the latter condition, because it ignores the opposing magnetic flux $Phi_L$ generated by the current induced in the loop.