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A photoresistor or light-dependent resistor (LDR) or photocell is a light-controlled variable resistor.
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circuit analysis of DC-source, inductance and modulated resistance
You won't (easily) get a closed form for \$\int e^{p(t)}dt\$.
The solution to the differential equation that you wrote is:
$$i(t)=\left(\frac{V}{L}\right)e^{\frac{-R_{mod}\sin(\omega t)}{L\omega}-\f …