a) A simple model for the shape of a tsunami is given by dW dx where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point offshore. By inspection, find all constant solutions of the DE. (Enter your answers as a comma-separated list W = 0,2 = W√4-2W, W(x) = ✓ b) Solve the differential equation in part (a). A CAS may be useful for integration. (Use C for the constant of integration.) c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition W(0) = 2. W
a) A simple model for the shape of a tsunami is given by dW dx where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point offshore. By inspection, find all constant solutions of the DE. (Enter your answers as a comma-separated list W = 0,2 = W√4-2W, W(x) = ✓ b) Solve the differential equation in part (a). A CAS may be useful for integration. (Use C for the constant of integration.) c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition W(0) = 2. W
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) A simple model for the shape of a tsunami is given by
dW
dx
= W√4-2W,
where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point offshore. By inspection, find all constant solutions of the DE. (Enter your answers as a comma-separated list.)
W = 0,2
(b) Solve the differential equation in part (a). A CAS may be useful for integration. (Use C for the constant of integration.)
W(x) =
-3
X
(c) Use a graphing utility to obtain the graphs of all solutions that satisfy the initial condition W(0) = 2.
W
-3
W
2
W
A
-3
3
W
3
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