hello, i desperately need help with differential equations- newton's law of cooling

i need to solve this D.E.........

dT/dt= -k(T-8)+H where k is a positive constant and h=1........

when t=0 T=16 PLEASE HELP ME!!!!!!!!!!!!!!!!!!!

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- Sep 2nd 2007, 01:46 AMpassarezurgent help needed with differential equations
hello, i desperately need help with differential equations- newton's law of cooling

i need to solve this D.E.........

dT/dt= -k(T-8)+H where k is a positive constant and h=1........

when t=0 T=16 PLEASE HELP ME!!!!!!!!!!!!!!!!!!! - Sep 2nd 2007, 04:49 AMtopsquark
$\displaystyle \frac{dT}{dt} = -k(T - 8) + H$

$\displaystyle \frac{dT}{dt} + kT = 8k + H$

The homogeneous equation is

$\displaystyle \frac{dT}{dt} + kT = 0$

and has a solution

$\displaystyle T_h(t) = Ae^{-kt}$

The particular solution will be of the form

$\displaystyle T_p(t) = B$

since the RHS of the differential equation is simply a constant. You can plug this into the original differential equation to get a value for B in terms of k and H.

Thus the general solution of this equation will be:

$\displaystyle T(t) = Ae^{-kt} + B$

where A is a constant to be fit to your initial conditions.

-Dan