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2nd order ODE (Control Systems)

ChemEng

New member
Jan 22, 2014
1
I'm trying to solve this equation analytically, but I can't even find the auxiliary equation or general solution!

wGsp94E.png

Km = 0.5
C*e = 0
K2 = 0.03
K1 = 0.05
x* = 49
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,197
What is $\tau$ and what is $\zeta$? If they do not depend on $t$, then this equation is fairly straight-forward (just assume $C_{m}=e^{kt}$, plug in, and solve for $k$, followed by finding a particular solution of the form $C_{m}=A$.)
 

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
1,404
I'd also advise substituting the values for your parameters, the equation will be much easier to read at least...