Differential Equations: Second Order Equations

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  • #1
peace-Econ
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Homework Statement



Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
LCKurtz
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Since you didn't show us what you have tried, instead of answering your question directly, I will ask you this:

Can you solve this de:

y'' - 4y' + 4y = e2t

and if so, what method would you use?

Hint: This isn't an idle question.
 
  • #3
HallsofIvy
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Homework Statement



Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions.

Homework Equations





The Attempt at a Solution

If those functions were independent, this would be impossible but [itex]e^{-t+ 1}= e^{-t}e^1= e e^{-t}[/itex], a constant times [itex]e^{-t}[/itex] so you really have only two independent solutions.

Do you know what the "characteristic equation" of a linear differential with constant coefficients is? Such an equation will have [itex]e^{ax}[/itex] and [itex]e^{bx}[/itex] as independent solutions if and only if its characteristic equation is [itex](r- a)(r- b)= 0[/itex].
 
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