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Homework Help: Solution to inhomogenous linear equation

  1. Sep 1, 2010 #1
    How do I show the difference of two solutions of an inhomogenous linear equation Lu=g with the same g is a solution of the homogenous equation Lu=0.

    Your help is much appreciated.

    thanks a lot.
     
  2. jcsd
  3. Sep 1, 2010 #2
    Can you please clarify what you mean. What two solutions ?

    Are you saying you have a system where Lu=g and Lu = 0 ?
     
  4. Sep 1, 2010 #3
    Hi thanks for the response.

    Yes, there are two systems Lu= 0 and Lu=g. I read in a book that the consequence of linearity is that if you add a homogenous solution to and inhomogenous solution , you get an inhomogeneous solution, you get an inhomogenous solution. They have not explained why?
     
  5. Sep 1, 2010 #4

    Mark44

    Staff: Mentor

    This is pretty straightforward. Assume that u1 and u2 are solutions to to the nonhomogeneous linear differential equation Lu = g.

    What can you say about L(u1 - u2)?
     
  6. Sep 1, 2010 #5
    Mark44,

    beautifully explained.

    so L(u1 - u2) = L(u1) - L(u2) = 0 ? Am I right?
     
  7. Sep 1, 2010 #6

    Mark44

    Staff: Mentor

    Yes. Make sure that you add what this says about u1 - u2.
     
  8. Sep 2, 2010 #7
    The solution to inhomogeneous equation of
    L[tex]\underline{u}[/tex]=[tex]\underline{g}[/tex]
    is the parametric solution of L[tex]\underline{u}[/tex]=[tex]\underline{0}[/tex] + [tex]\underline{g}[/tex]
     
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