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Deducing the order of an ODE from its solution curve

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0

$begingroup$

What is the smallest possible order of a linear, homogeneous ODE with constant coefficients which the following curves are solutions of?

My thoughts: different frequencies for the oscillations imply minimum order $4$ because I need to solve two sets of $r^2+br+c=0$ characteristic equations. However I do not know what to do about the constant solution.

ordinary-differential-equations

share|cite|improve this question

edited Mar 20 at 13:08

NetUser5y62

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts?
  $endgroup$
  – Artem
  Mar 20 at 12:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The constant solution tells you that the ODE doesn't have a term like $cy$ with $c neq 0$. It won't tell you much about the order, except that it is at least order $1$.
  $endgroup$
  – Gary Moon
  Mar 20 at 13:54
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

What is the smallest possible order of a linear, homogeneous ODE with constant coefficients which the following curves are solutions of?

My thoughts: different frequencies for the oscillations imply minimum order $4$ because I need to solve two sets of $r^2+br+c=0$ characteristic equations. However I do not know what to do about the constant solution.

ordinary-differential-equations

share|cite|improve this question

edited Mar 20 at 13:08

NetUser5y62

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts?
  $endgroup$
  – Artem
  Mar 20 at 12:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The constant solution tells you that the ODE doesn't have a term like $cy$ with $c neq 0$. It won't tell you much about the order, except that it is at least order $1$.
  $endgroup$
  – Gary Moon
  Mar 20 at 13:54
  
  
  

  
  
  
  

add a comment | 

$begingroup$

What is the smallest possible order of a linear, homogeneous ODE with constant coefficients which the following curves are solutions of?

My thoughts: different frequencies for the oscillations imply minimum order $4$ because I need to solve two sets of $r^2+br+c=0$ characteristic equations. However I do not know what to do about the constant solution.

ordinary-differential-equations

share|cite|improve this question

edited Mar 20 at 13:08

NetUser5y62

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

$endgroup$

share|cite|improve this question

edited Mar 20 at 13:08

NetUser5y62

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

share|cite|improve this question

edited Mar 20 at 13:08

NetUser5y62

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215

asked Mar 20 at 12:38

NetUser5y62NetUser5y62

525215