t=var('t')
I=function('I',t)
DE = 5*diff(diff(I,t),t) + 20*diff(I,t) + 100*I - 425*40*cos(40*t)
I(t)=desolve (DE,[I,t])
I(0)==0
de(t)=diff(I,t)
de(0)==0
k1,k2=var('k1,k2')
solve([I(0)==0,
       de(0)==0],k1,k2)

print I.subs(k1 = (-1377/1261), k2 = (2686/1261))