Exercise 4. Let f be a differentiable function of one variable. Show that u(x, t) = f(x - vt) is a solution to the one-dimensional transport equation ди du Ət da Use this fact to find the solution that satisfies the initial condition 1 22 +1 +v = 0. u(x,0) = [Suggestion: Set t = 0 above and solve for f.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 3E
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Exercise 4. Let f be a differentiable function of one variable. Show that
u(x, t) = f(x - vt)
is a solution to the one-dimensional transport equation
ди ди
+v-
Ət da
Use this fact to find the solution that satisfies the initial condition
u(x,0) =
=
[Suggestion: Set t = 0 above and solve for f.]
-
0.
1
22 +1
Transcribed Image Text:Exercise 4. Let f be a differentiable function of one variable. Show that u(x, t) = f(x - vt) is a solution to the one-dimensional transport equation ди ди +v- Ət da Use this fact to find the solution that satisfies the initial condition u(x,0) = = [Suggestion: Set t = 0 above and solve for f.] - 0. 1 22 +1
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