Need help with differential equation
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Need help with differential equation

[From: ] [author: ] [Date: 11-11-13] [Hit: ]
You will need to split the left side into partial fractions.Can you finish from there? Remember that Tm is a constant. The first three terms on the left will integrate to natural logarithms and the fourth to arctan.-Could you tell me if this is right? I got A ln(t)+Bln(t)+Cln(t)/2+1/T^2m[t… (T/Tm)]=kt+C.......
According to Stefan's law of radiation, the absolute temp. T of a body cooling in a medium at constant absolute temp. (T sub m) or Tm is given by:

dT/dt=k(T^4-T^4sub m) Solve the differential equation

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This is a variables separable first order differential equation.

dT/dt = k(T^4 - Tm^4) ----> INT dT/(T^4 - Tm^4) = INT k dt

Integrate each side separately. You will need to split the left side into partial fractions.
A/(T - Tm) + B/(T + Tm) + CT/(T^2 + Tm^2) + D/(T^2 + Tm^2)

Can you finish from there? Remember that Tm is a constant. The first three terms on the left will integrate to natural logarithms and the fourth to arctan.

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Could you tell me if this is right? I got A ln(t)+Bln(t)+Cln(t)/2+1/T^2m[t… (T/Tm)]=kt+C....
then I divided both sides by t (basically just put all that over t)....is this my final answer k=this answer?

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