2. Deduction is a matter of course. For all variables, the derivative is about time t, and the constants such as resistance, capacitance and inductance remain unchanged.
3. If you feel that the mathematical method is not easy to understand, you can try the "equivalent resistance method". The impedance of the capacitor is expressed as Cs, and the impedance of the inductor is expressed as 1/(Ls). Simplify the circuit diagram (mainly simplifying the resistance), get the relationship between input and output (or other variables) by using the relationship between voltage and current, and then get the answer by Laplace inverse transformation under zero initial condition.
4.