Analizar la estabilidad de la ecuación: (dW)/(dx) =W√(4-2W)

Question

Analizar la estabilidad de la ecuación:

`(dW)/(dx) =W√(4-2W)`

Answer 1

Find the equilibrium solutions.

`W √(4 - 2W) = 0 \\\\ W = 0 \text{ or } √(4 - 2W) = 0 \\\\ W = 0 \text{ or } W = 2`

Note that
`(dW)/(dx)` is undefined if
`W>2`.

When
`W<0`, we have
`(dW)/(dx) < 0`.

When
`0 < W < 2`, we have
`(dW)/(dx) > 0`.

The change in sign from negative to positive as
`W` passes through 0 indicates that
`W=0` is a stable equilibrium solution.