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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- September 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!!!!!!!!!!!!!!!!!!! - September 2nd 2007, 04:49 AMtopsquark

The homogeneous equation is

and has a solution

The particular solution will be of the form

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:

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

-Dan