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About Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience
Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

You are here: Experts > Science > Mathematics > Differential Equations > Simultaneous differential equations

Differential Equations - Simultaneous differential equations

Expert: Abe Mantell - 7/15/2009

Question
Respected Sir,

I'm currently pursuing a project on the cycle times of mist flow to a Nutrient mist reactor in which growth of roots are undertaken. I've been able to formulate a set of differential equations which however have to be solved simultaneously. I did try to solve the same in MATLAB but it is displaying some error which I could not comprehend. I have been trying to solve them manually as well for quite some time now with no results.
I was hoping you could help me get the solution to these three equations..

These are as given below...

d(M_r)/M_r = a*C*(dt)

d(H)/dt = b*((M_r/M_r_o)^alfa)-(k*(H-Hsat))

d(C)/dt = (b/Hsat)*((M_r/M_r_o)^alfa)*(C_f-C)-(d*(C*M_r)/(H-Hsat))

t is time which is the independant variable & M_r, H and C are the dependant variables.

M_r = mass of roots at time t.
M_r_o = mass of roots at time t = 0. (Constant)

C = nutrient concentration at time t.
C_f = concentration of nutrients supplied initialy. (Constant)

H = liquid hold up at time t.
Hsat = liquid hold up initialy. (Constant)
a, b, d, k, alfa are constants.

Your advice in this regard would be highly appreciated.
Eagerly awaiting your reply.

Thanking you,

Debraj Ghosh

Answer
Hello Debraj,

Sorry for my delay. I tried to get my CAS (computer algebra system),
Maple 12, to solve your system of DE's...but it failed.

Perhaps if you could furnish some actual values for the parameters,
it would be helpful.

Can you?

TTYL, Abe

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