A rod of lengthn coincides with the interval [0, T] on the x-axis. The rod has initial temperature f(x) = 5 for 0 < x < a with the ends at temperature zero for all t > 0. Assume the rod satisfies all the assumptions of the heat equation with a constant a² of three. Set up an initial-boundary value problem for the temperature u(x, t), then find the solution, the temperature u(x,t).

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Q: 3. Find the position function x(t) given the acceleration a(t), the initial velocity vo = %3D v(0),…

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Q: the differential equation that describes the motion.

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Q: etermine whether the function u(x, t)=ecos() is a solution of the heat conduction equa- on u₁=a²uxx-

A:

Q: 7. An outdoor swimming pool loses 0.05% of its water volume every day it is in use, due to losses…

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Q: Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at…

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Q: Consider the heat equation ƏT Ət ᏛᎢ . 7 əx² 0≤x≤n. Solve the equation using separation of variables…

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Q: homogeneous solution to the second order constant coefficient ODE’s. Solution must be real.

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Q: Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams)…

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Q: (4) Suppose the acceleration of an object is given by a(t) = t m/s. Its initial velocity is v(0) = 5…

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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.