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Steady state solution of a differential equation 
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#1
Dec1211, 12:38 AM

P: 258

1. The problem statement, all variables and given/known data
Hey. I am taking a matlab class and my instructor is absolutely horrendous. he does not teach us anything, but asks questions on everything. I'm having a problem with the following question: http://imageshack.us/photo/myimages/641/55811089.png/ What is a steady state solution of a differential equation? How can i solve the attached problem in matlab? Thanks a lot. 2. Relevant equations 3. The attempt at a solution 


#2
Dec1211, 08:29 AM

P: 1,666

[tex]\left\{\left\{y\to \text{Function}\left[\{t\},e^{\left(\frac{2}{3}\frac{\sqrt{19}}{3}\right) t} C[1]+e^{\left(\frac{2}{3}+\frac{\sqrt{19}}{3}\right) t} C[2]+\frac{36 (17 \text{Cos}[2 t]8 \text{Sin}[2 t])}{\left(59+4 \sqrt{19}\right) \left(59+4 \sqrt{19}\right)}\right]\right\}\right\}[/tex] so I don't see the relevance of that expression Acos(bt+c). Also, looking at the solution I don't see how it will ever reach a steady state. 


#3
Dec1211, 11:03 AM

HW Helper
Thanks
PF Gold
P: 7,563




#4
Dec1311, 06:46 AM

HW Helper
P: 1,965

Steady state solution of a differential equation
Maybe the question is referring to the way such systems can typically have a transient initial part that dies down and longterm settles down into a regular periodic 'forced' oscillation, that long term part being called the 'steady state'. You almost must have had examples in math and physics already.
Your LHS expressed in operator terms easily factorises into real factors with exponential solutions I think. (Though it alarms me to see one positive and one negative, making me wonder if this has such a steady state; maybe I am mistaken somehow.) Solve the equation and see how it behaves longterm. Oh, I see you have. The solution does not look right to me, but it does seem to have the problem I mentioned. 


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