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Sage Second Order Differential Issue

utoft May 31st, 2013 40 Never
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  1. Vout,t = var("Vout,t")
  2.  
  3. #The known variables
  4. L = 1e-3
  5. C = 1e-9
  6. Vin = 5
  7. R = 1e3
  8.  
  9. Vout = function("Vout",t)
  10. equation = L*C*diff(Vout,t,2) + R*C*diff(Vout,t) + Vout == Vin
  11. generalSolution = desolve(equation,Vout,ivar=t)
  12. print "General Solution :", generalSolution
  13. show(generalSolution)
  14. specificSolution = desolve(equation,Vout,ivar=t,ics=[0,0,0])
  15. print "Specific Solution :", specificSolution
  16. show(specificSolution)
  17.  
  18. #Plotting
  19. plotMax = 2e-5
  20. plot1 = plot(specificSolution,[t,0,plotMax],rgbcolor=[0,0,0]) #Differential equation
  21. plot1 += plot(Vin*0.1,[t,0,plotMax],rgbcolor=[0,0,1]) #10% line
  22. plot1 += plot(Vin*0.9,[t,0,plotMax],rgbcolor=[0,0,1]) #90% line
  23. show(plot1)
  24.  
  25. #Find the local maximum
  26. findMax = find_local_maximum(specificSolution,1e-6,5e-6)
  27. print "Local max =", findMax
  28.  
  29. print "### First Issue ###"
  30. ### FIRST ISSUE ###
  31. ### Normally i would take the differential and set it to zero
  32. findMax2 = solve(diff(specificSolution,t) == 0,t)
  33. print "Local max2", findMax2 ## Result is obviously wrong. It should match findMax
  34.  
  35. print "### Second Issue ###"
  36. ### SECOND ISSUE ###
  37. #First as i usually would do
  38. print "\t 10% = ",solve(specificSolution==Vin*0.1,t)
  39. print "\t 90% = ",solve(specificSolution==Vin*0.9,t)
  40.  
  41. ## i found this somewhere, but it didn't help
  42. func(t) = specificSolution
  43. print "\t 10% = ",solve(func(x)==Vin*0.1,x)
  44. print "\t 90% = ",solve(func(x)==Vin*0.9,x)
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