math007
  • math007
how to solve a non-homogeneous equation? I do not like to guess, is there another way I can solve these equations?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
equation?
myininaya
  • myininaya
yes you cannot solved every differential equation the same way
math007
  • math007
y"-2y'-3y=3e^2x

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myininaya
  • myininaya
first let's pretend it is homogeneous. so we have r^2-2r-3=0 which gives r=-1 and r=3 so we have y=Ae^(3t)+Be^(t) for any constant. But this doesn't solve the homogeneous solution. So the only way I know how to solve this differential equation is to choose y=Ae^(2t) and find what A is. But this is that guessing thing you were talking about.
myininaya
  • myininaya
oops y=Ce^(3t)+Be^(-t)
math007
  • math007
yes, I understand this much. Now the problem is finding the right side, the non homog. part. How do I go about solving the right side?

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