Please show as much work as possible, thank you! Consider an initially passive R

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Please show as much work as possible, thank you!

Consider an initially passive RC circuit (no inductance) with a battery supplying e0 volts. If the switch is closed at time t = a and opened at time t = b > a (and left open thereafter), the current in the circuit satisfies the initial value problem:

Ri′ + (1/C)i = e0δ(t–a) – e0δ(t-b); i(0) = 0

Solve this problem if R = 100 Ω, C = 10-4F, e0 = 100 V, a = 1(s) and b = 2(s). Show that i(t) > 0, if 1 < t < 2 and that i(t) < 0 if t > 2.

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