Differential equations question:

y' = ay - b(y)^(1/2)

a 0, b 0

One of the critical points for this differential equation is 0 (you can tell just by looking at it).

Here's the problem, I have to determine if this critical point is stable, unstable, or semistable.

But how do I determine this since y cannot be a negative number because of the square root? In this form, I can only do the first derivative test on the positive side of 0, but not the negative. So I'm confused, can someone please explain how you figure this out?

Question

Differential equations question:

y' = ay - b(y)^(1/2)

a > 0, b > 0

One of the critical points for this differential equation is 0 (you can tell just by looking at it).

Here's the problem, I have to determine if this critical point is stable, unstable, or semistable.

But how do I determine this since y cannot be a negative number because of the square root? In this form, I can only do the first derivative test on the positive side of 0, but not the negative. So I'm confused, can someone please explain how you figure this out?

anonymous · Answer

$$y' = ay-b \sqrt{y}$$