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# Partial Differential Equations

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1. Consider the first order PDE,

∂u/∂t = ct(∂u/∂x) -&#8734; < x < &#8734; c does not equal 0

a) Find the fundamental solution

b) Use the fundamental solution and convolution to find a formula for the solution to:

∂u/∂t = ct(∂u/∂x) -&#8734; < x < &#8734; c does not equal 0 u(x,0) = f(x)

c) Use the method of characteristics to find the solution to part b.(Make sure your answers agree)

https://brainmass.com/math/partial-differential-equations/partial-differential-equations-functions-180856

#### Solution Preview

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Please find the solution in the attached file.

1. Consider the first order PDE,

∂u/∂t = ct(∂u/∂x) -∞ < x < ∞ c does not equal 0

a) Find the fundamental solution

b) Use the fundamental solution and convolution to find a formula for ...

#### Solution Summary

This finds the fundamental solution of a first-order partial differential equation, and uses that solution and convolution, as well as method of characteristics, in another problem. The expert uses the method of characteristics to find the function.

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