2.) The flow of heat along a thin conducting bar is governed by the one-dimensional heat equation given by du partial differential equation where u(x, t) is a measure of the temperature at a location x on the at bar at time t and positive constant k is related to the conductivity of the material. a.) Consider the function u(x, t) = 10e-tsin(x). Assuming k = 1, find the following partials: du at du b.) In the space below, show that u(x, t) satisfies the heat equation with k = 1.

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The given function is g(x,y)=lnx2+y23 We have to find the gradient of the function and maximum value…

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: a) Find the total differential for the following function z = f(x,y) = xy + y xb) Use Chain Rule for…

A:

Q: 5(c) Calculate the total differential of the following function: 1+ uv 1- u/v g(u, v) =

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Q: Find all second order partial derivatives of the given functions f(x, y) = cos(2xy? - 3x²y³)

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A:

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.