Sample Final Exam Problems

# Sample Final Exam Problems - Problem 1(5 5 10 Consider the...

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Problem 1 (5+5+10)  Consider  the  first  order  differential  equation  (DE)  ( ) 0 dy ax by bx cy dx + + + =   where   , , a b c  are  constants. a.  Is the  above  equation  linear  or nonlinear?  Explain  your  answer. b. Is there  an  integrating  factor   ( ) x μ  of the  DE?  If so,  find   ( ) x μ . c. Solve the  differential  equation. Problem 2 (5+5+15) For  the  electric,  series  circuit  shown, a. find  the  governing  differential  equation  for the  charge   ( ) q t  at  time   t  in the  circuit  in terms  of  R C L  and   V ( t ) b. Is the  solution  of the  above  differential  equation   stable  or unstable  for  R, C, L  > 0?  Recall  that  a  solution  is unstable  if it becomes  unbounded  as  time   t  increases.  Describe  the  steady  state  behavior  of the   current   I ( t ) for  R, C, L  > 0 and   ) cos( ) ( t te t V t - =  volts.

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• Spring '08
• KING
• Boundary value problem

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