How to solve this equation?

[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

Answer 1

[Walter Roberson]

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

[myeong su kim]

C0 = 8.04*10^7;

U = 2.38*10^8;

M = 1.91*10^-15;

Phi = 1.0*10^14;

P = 0.24;

Q = 27354;

R = 1.98;

T = 632;

t = 1:0.1:100;

Cl = 1

Cl =

1

??? Error using ==> mtimes

Inner matrix dimensions must agree.

Error in ==> Untitled2 at 11

diff(s(t),t) = (C0+U*(M*Phi)^P)*t*exp(-Q*t/(R*T))

and,, i wnat plot(t,function)

help plz

[Walter Roberson]

You cannot use that form of diff() at the MATLAB level, and you need the symbolic toolbox to solve the differential equation symbolically.

s = -R*T*(R*T+Q*t).*(Co+U*(M*Phi)^P).*exp(-Q*t/(R*T))/Q^2 + C1

Notice the added "." before the "*". For greater security you could convert all of the "*" to ".*".

Remember too that C1 is an arbitrary constant of integration, so it is symbolic here and must remain symbolic unless you have a boundary condition that can be used to define its value.