(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

[itex]\int \frac{dy}{y\sqrt{4-2y}} = -tanh(\frac{1}{2}\sqrt{4-2y})[/itex]

3. 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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# Homework Help: Check my separable diff EQ work?

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