First order system DE -> second order

  • Thread starter tourjete
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  • #1
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first order system DE --> second order

Homework Statement



Find a second-order DE for x alone that is equivalent to this system.


Homework Equations



dx/dt = 2x-y

dy/dt = -x

The Attempt at a Solution



I honestly have no clue where to start; in class we pretty much only stuck to springs when discussing second order equations.

Do I have to integrate the two given equations with respect to t so I have the t's in the equation? Or should I differentiate so I have a second derivative and hence a second order equation?
 

Answers and Replies

  • #2
Dick
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It's not that complicated. For example, just solve the second equation for x and substitute that into the first equation.
 
  • #3
fzero
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You can differentiate the first equation and then use the 2nd to eliminate y.
 
  • #4
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Thanks guys! I did what fzero sugested and just want to make sure I did it right. I solved the second equation for y so I could eliminate it from the other one and got y = -xt.

I then plugged that into the first equation to get dx/dt = 2x + xt + C. Differentiating with respect to t i gotthat the second derivative is x + C. Is this right? It seems simplistic given the derivatves that were given.
 
  • #5
fzero
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What I meant was take the derivative of the first equation to get

[tex] \frac{d^2x}{dt^2} = 2\frac{dx}{dt}-\frac{dy}{dt}, [/tex]

then use the 2nd to write this as

[tex] \frac{d^2x}{dt^2} = 2\frac{dx}{dt}+x. [/tex]
 

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