A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature f(x) = 200 degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1). Put us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

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Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: A thin bar of length L= 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: A thin bar of length L-3 meters is situated along the x axis so that one end is at x =0 and the…

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Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.