Sage Second Order Differential Issue

Vout,t = var("Vout,t")

#The known variables
L = 1e-3
C = 1e-9
Vin = 5
R = 1e3

Vout = function("Vout",t)
equation = L*C*diff(Vout,t,2) + R*C*diff(Vout,t) + Vout == Vin
generalSolution = desolve(equation,Vout,ivar=t)
print "General Solution :", generalSolution
show(generalSolution)
specificSolution = desolve(equation,Vout,ivar=t,ics=[0,0,0])
print "Specific Solution :", specificSolution
show(specificSolution)

#Plotting
plotMax = 2e-5
plot1 = plot(specificSolution,[t,0,plotMax],rgbcolor=[0,0,0]) #Differential equation
plot1 += plot(Vin*0.1,[t,0,plotMax],rgbcolor=[0,0,1]) #10% line
plot1 += plot(Vin*0.9,[t,0,plotMax],rgbcolor=[0,0,1]) #90% line
show(plot1)

#Find the local maximum
findMax = find_local_maximum(specificSolution,1e-6,5e-6)
print "Local max =", findMax

print "### First Issue ###"
### FIRST ISSUE ###
### Normally i would take the differential and set it to zero
findMax2 = solve(diff(specificSolution,t) == 0,t)
print "Local max2", findMax2 ## Result is obviously wrong. It should match findMax

print "### Second Issue ###"
### SECOND ISSUE ###
#First as i usually would do
print "\t 10% = ",solve(specificSolution==Vin*0.1,t)
print "\t 90% = ",solve(specificSolution==Vin*0.9,t)

## i found this somewhere, but it didn't help
func(t) = specificSolution
print "\t 10% = ",solve(func(x)==Vin*0.1,x)
print "\t 90% = ",solve(func(x)==Vin*0.9,x)