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## Homework Statement

In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms

Find vC(t) for t≥0.

Express your answer in terms of t, where t is in milliseconds.

## Homework Equations

i=c*dv/dt

## The Attempt at a Solution

the only part of this problem i am not getting is solving for the constants with the given initial conditions... the 2 roots to the differential equation are -5000. so:

v(t)=C_1*e^(-5000t)+C_2*t*e^(-5000t)

and

dv/dt [at t=0+]=-5000*C_1+C_2=i/c=(6*10^-3)A/(320*10^-9 F)=18750 volts/s

v(0)=C_1=15V

so C_2 -5000*15=18750...C_2=93750

but apparently C_2 is actually equal to 56250....If the equation was C_2-5000*15=-18750, then i would get 56250...where am i going wrong???