Undetermined coefficients

  • Thread starter cue928
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  • #1
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I'm working on undetermined coefficients for nonhomogeneous equations. I have an equation that is equal to 3xe^x. For an earlier one that was equal to e raised to 8x, I used Ae^8x; but on this one, obviously that won't work. I don't know what I should be looking at. I tried Axe^x but no dice on that one either. I know things are supposed to cancel but for two terms multiplied together, how does that work for cancelling purposes? Is it really just a guessing game as to what the form of the particular solution should be?
 

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  • #2
vela
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You want to use yp(x) = (Ax+B)ex. I'm assuming that these terms are independent of your homogeneous solutions.
 
  • #3
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They are, but how did you know how to use that formula? Our book suggests determining it is an educated guess but another book I use as a reference seems to suggest there are standard formulas. What should I be looking at in determining what to use? Thanks!
 
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