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disp('by kvl')
disp('Ldi/dt+Ri+1/c*integ(i)=V')
disp('given')
disp('V=1,R=3,L=1,C=0.5')
disp('Replacing di/dt with s and (di/dt)^2 with s^2')
disp('we get')
disp('s^2+3s+2')
s=poly(0,'s')
p=s^2+3*s+2
r=roots(p)
disp(r)
disp('therefore the current in general form is')
disp('i(t)=k1exp(-t)+k2exp(-2t)')
//k1 and k2 are constants and are evaluated by knowing inital conditions
disp('initial conditions are')
disp('di/dt at 0+ is V/L=1')
disp('i(t) at 0+ is 0')
disp('on solving we get k1=1,k2=-1')
t=0:0.1:2
i=exp(-t)-exp(-2*t)
subplot(221)
xtitle("exp(-t)")
plot2d(exp(-t))
subplot(222)
xtitle("exp(-2t)")
plot2d(exp(-2*t))
subplot(223)
xtitle("i")
plot2d(i)
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