- #1
ElijahRockers
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Homework Statement
A model for the shape of a tsunami is given by
[itex]\frac{dW}{dx} = W\sqrt{4-2W}[/itex]
where W(x) > 0 is the height of the wave expressed as a function of its position relative to a point off-shore.
Find the equilibrium solutions, and find the general form of the equation. Use graphing software to graph the direction field, and sketch all solutions that satisfy the initial condition W(0) = 2.
Homework Equations
[itex]\int \frac{dy}{y\sqrt{4-2y}} = -tanh(\frac{1}{2}\sqrt{4-2y})[/itex]
The Attempt at a Solution
i'm pretty sure the equilibrium solutions are w = 0,2
but i have never seen or used hyperbolic trig functions, so I guess I was just wondering if they work the same way as regular trig functions.
It doesn't seem hard, I guess I would just like someone to verify my answer for the general form:
[itex]W(x) = 2-2arctanh^2(-x+C)[/itex]
If anyone gets anything different let me know and I can show my work, thanks.
As for the sketching, as far as I can tell W(any x)=2 is a horizontal straight line, which seems pretty boring to sketch...
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