SDE Integration

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Does anyone know how to get the integration of the SDE below (Assume $\sigma \to 0$)?

$$\dfrac{\mathrm dS_t}{S_t}=(r_d-r_f)\mathrm dt+\sigma(t, S_t)\mathrm dW_t$$

Thank you in advance!

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If we assume $\sigma = 0$ then we will simply have an ODE : $S_t = S_0\exp((r_d - r_f)t)$. We will need more information on the volatility of the FX rate (i.e. local vol, stochastic vol)?

Thanks.