# Thread: Simple ODE.

1. ## 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

$\displaystyle \frac{dT}{dx} = -6$

In a simple model for the temperature of the rod, it is assumed that $\displaystyle \frac{dT}{dx}$ 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.

2. Originally Posted by Tweety
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

$\displaystyle \frac{dT}{dx} = -6$

In a simple model for the temperature of the rod, it is assumed that $\displaystyle \frac{dT}{dx}$ 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.
$\displaystyle \displaystyle \frac {dT}{dx} = -6$

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

$\displaystyle \displaystyle \Rightarrow T = -6x + C$

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

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### a metal rod is 60 cm long and is heated a

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