A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z). a.Show a differential equation derivation to...

A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z).
a.Show a differential equation derivation to describe the system
b.Make a sketch utilizing circuit diagram
c.Mention if the RC system in question above is
i.Time in-variant   / Time variant

ii.Non linear / linear
iii.Non-invertible / Invertible
iv. Non-causal / Causal

v. Have no memory /  Have memory

sytems.


d. d²b(z)/dz²
+ 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z)


Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above.
Where a(z) & b(z) is the input & output of the RC system respectively.
Considering an impulse of a(z)=δ(z) is applied to the system, determine the output b(z) of the system