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ODE problem

  1. Feb 5, 2006 #1
    Let x = x1(t), y = y1(t) and x = x2(t), y = y2(t) be any two solutions of the linear nonhomogeneous system.

    [tex] x' = p_{11}(t)x + p_{12}(t)y + g_1(t) [/tex]
    [tex] y' = p_{21}(t)x + p_{22}(t)y + g_2(t) [/tex]

    Show that x = x1(t) - x2(t), y = y1(t) - y2(t) is a solution of the corresponding homogeneous sytem.

    I am not sure what it is that I am suppose to do. Could anybody explain?
  2. jcsd
  3. Feb 6, 2006 #2


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    "Plug and chug". The "corresponding homogeneous system" is, of course, just the system with the functions g1(t) and g2(t):
    [tex]x'= p_{11}(t)x+ p_{12}(t)y[/tex]
    [tex]y'= p_{21}(t)x+ p_{22}(t)y[/tex]
    replace x with x1- x2, y with y1- y2 in the equations and see what happens. Remember that x1, x2, y1, y2 satisfy the original equations themselves.
    Last edited by a moderator: Feb 6, 2006
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