I\'ve been working on this problem all day and have tried a few solutions that I thought should work for sure, please help! Solution using KCL: (v/R)+(1/L)*integration of v*dt +C*dv/dt=0 differenting one more time: (1/R)*dv/dt + (1/L)*v + C*d^2v/dt^2=0 putting the values: 5*10^(-6)*v\'\'+10^(-2)*v\'+5*v=0 where v\'=dv/dt and v\'\'=d^2v/dt^2 now assuming v=A*exp(m*t) where A and m are two constants then 5*10^(-6)*m^2+10^(-2)*m+5=0 m=-1000(double root) then v(t)=(k1+k2*t)*exp(-1000*t) where t is in seconds now writing it in milliseconds, v(t)=(k1+k2*t)*exp(-t) now at t=0 ,v(t)=25 volts so k1=25 at t=0, current through inductor =-0.3 A so L*dv/dt=-0.3, at t=0 0.2*(-k1+k2)=-0.3 -25+k2=-1.5 k2=23.5 so v(t)=(25+23.5*t)*exp(-t) where t is in milliseconds .

1. I've been working on this problem all day and have tried a few solutions that I thought should
work for sure, please help!
Solution
using KCL:
(v/R)+(1/L)*integration of v*dt +C*dv/dt=0
differenting one more time:
(1/R)*dv/dt + (1/L)*v + C*d^2v/dt^2=0
putting the values:
5*10^(-6)*v''+10^(-2)*v'+5*v=0
where v'=dv/dt
and v''=d^2v/dt^2
now assuming v=A*exp(m*t)
where A and m are two constants
then 5*10^(-6)*m^2+10^(-2)*m+5=0
m=-1000(double root)
then v(t)=(k1+k2*t)*exp(-1000*t)
where t is in seconds
now writing it in milliseconds,

2. v(t)=(k1+k2*t)*exp(-t)
now at t=0 ,v(t)=25 volts
so k1=25
at t=0, current through inductor =-0.3 A
so L*dv/dt=-0.3, at t=0
0.2*(-k1+k2)=-0.3
-25+k2=-1.5
k2=23.5
so v(t)=(25+23.5*t)*exp(-t)
where t is in milliseconds