MATLAB: How to solve this equation

differential equationMATLABplot

[EDIT: 20110604 23:41 CDT – reformat – WDR]
hi i`m trying to solve this differential equation
  1. ds/dt=[Co+U(MΦ)^P]exp(-Q/RT)
ds/dt = oxidation rate [μm/day]
Co =  8.04×10^7 [μm/day] 
U = 2.38×10^8 [μm/day]
M = 1.91×10^-15 [cm^2-s/neutron]
Φ = 1.0×10^14 [neutron/cm^2-s]
P = 0.24
Q = 27,354 cal/mol
R = 1.98 cal/mol-k
T = 632 K
I want to plot a differential equation
please,,,, help

Best Answer

s(t) = (Co+U*(M*Phi)^P)*exp(-Q/RT) * t + C1
where C1 is an arbitrary constant of integration.
Perhaps your original equation needs a "t" on the right-hand side?
Also, please clarify whether -Q/RT is -Q/R * T, or -Q/(R*T)
If your expression happens to be
diff(s(t), t) = (Co+U*(M*Phi)^P)*exp(-Q*t/(R*T))
then the solution is still fairly simple,
s(t) = -R*T*(Co+U*(M*Phi)^P)*exp(-Q*t/(R*T))/Q + C1
It doesn't start to get interesting until you are asking for something like
diff(s(t), t) = (Co+U*(M*Phi)^P)*t*exp(-Q*t/(R*T))
which solves as
s(t) = -R*T*(R*T+Q*t)*(Co+U*(M*Phi)^P)*exp(-Q*t/(R*T))/Q^2 + C1
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