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Math Help - urgent help needed with differential equations

  1. #1
    passarez
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    Question urgent 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!!!!!!!!!!!!!!!!!!!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by passarez View Post
    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!!!!!!!!!!!!!!!!!!!
    \frac{dT}{dt} = -k(T - 8) + H

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

    The homogeneous equation is
    \frac{dT}{dt} + kT = 0
    and has a solution
    T_h(t) = Ae^{-kt}

    The particular solution will be of the form
    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:
    T(t) = Ae^{-kt} + B
    where A is a constant to be fit to your initial conditions.

    -Dan
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