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Math Help - Simple ODE.

  1. #1
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    Simple ODE.

    A metal rod is 60cm long and is heated at one end. The temperature at a point on the road at a distance xcm from the heated end is denoted by T degrees Celsius At a point half way along the rod T= 290 and

     \frac{dT}{dx} = -6

    In a simple model for the temperature of the rod, it is assumed that  \frac{dT}{dx} has the same value at all points in the rod. For this model, express T in terms of x and hence determine the temperature difference between the end of the rod.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Tweety View Post
    A metal rod is 60cm long and is heated at one end. The temperature at a point on the road at a distance xcm from the heated end is denoted by T degrees Celsius At a point half way along the rod T= 290 and

     \frac{dT}{dx} = -6

    In a simple model for the temperature of the rod, it is assumed that  \frac{dT}{dx} has the same value at all points in the rod. For this model, express T in terms of x and hence determine the temperature difference between the end of the rod.
    \displaystyle \frac {dT}{dx} = -6

    \displaystyle \Rightarrow \int ~dT = - \int 6~dx

    \displaystyle \Rightarrow T = -6x + C

    now just plug in \displaystyle T = 290, ~x = 30 to solve for \displaystyle C, and you have it. The rest should be easy
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