## Consider the autonomus equation $\frac{dy}{dt}=-2(y-1)(y-2)(y-a)^2$

Consider the autonomus equation $$\frac{dy}{dt}=-2(y-1)(y-2)(y-a)^2$$, where $$a$$ is any real number.

Then,

$$(1)$$ Plot the phase diagram showing the solution curves.

$$(2)$$ show that new solution can be generated from the old solutions (in $$(a)$$) by time shifting i.e, replacing $$y(t)$$ by $$y(t-t_0)$$.

$$(a)$$ I have drawn the phase plot showing the solutions.

Please help me with the part $$(b)$$.

If we replace $$y(t)$$ by $$y(t-t_0)$$, then we have

$$\frac{dy(t-t_0)}{dt}=-2(y(t-t_0)-1)(y(t-t_0)-2)(y(t-t_0)-a)^2$$.

How to confirm that we get a new solution?

Help me

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