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Linear dynamical systems

  • Thread starter johnaphun
  • Start date
  • #1
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Homework Statement



Convert the differential equation for x,

x''' + 2(x''2) = 0

Into a system of first order differential equations. Put the system in vector form

Homework Equations





The Attempt at a Solution



I'm able to do this for simpler DE's but I can't seem to find an answer for this one. Do i need to do anything different because of the 3rd derivative?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
tiny-tim
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hi johnaphun! :smile:

what's the difficulty? :confused:

put a = x'' and solve, then put v = x' and solve
 
  • #3
HallsofIvy
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Same thing except that I tend to prefer to use letters near the beginning of the alphabet, like "a", to represent constants, letters near the end, like "x", to represent variables.

Since your equation is [itex]x'''+ 2(x'')^2= 0[/itex], let y= x' and z= y'= x'' so that x'''= z'. Now, [itex]x'''+ 2(x'')^2= z'+ 2z^2= 0[/itex], [itex]y'= z[/itex], and [itex]x'= y[/itex].
 
  • #4
tiny-tim
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Same thing except that I tend to prefer to use letters near the beginning of the alphabet, like "a", to represent constants, letters near the end, like "x", to represent variables.
Normally, I'd agree! :smile: … but this equation looked to me like a dynamical equation, with x being distance, so I preferred the familiar form of x' = v, v' = a. :wink:
 

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