Question

How to differentiate the autonomous DE: y' =y^2(4-y^2)?

Answer 1

So I'm trying to check concavity, and trying to differentiate the DE above. The RHS is just the product of two functions, so I'd assume you would use the product rule? Does implicit differentiation come into play at all?

Answer 2

for implicit differentiation... no.. very off topic.. do you have to provide a graph?

Answer 3

I'm just suppose to sketch solutions curves to the above DE.

Answer 4

ah you need equilibrium !

Answer 5

When does implicit differentiation come into play?

Answer 6

Yeah, I found the equilibrium solutions to be y=0, y=2, and y=-2

Answer 7

when does implicit come to play? neverrrrrrrr! I took a DE course last semester. I never used that.

Answer 8

I found all of them to be semi-stable. Now I'm just trying to diff. in order to get the formula for concavity.

Answer 9

ok so draw the graph with horizontal lines 0 2 and -2
then we need to pic a point in between those ranges to see if it's stable, semistable or unstable.

Answer 10

Oh, okay.

Answer 11

oh then afterwards you have to find the derivative.

Answer 12

Yeah, that's why I need help diff. the DE. I was just confused on how to differentiate it.

Answer 13

umm you could just distribute the y^2 and then take the derivative...much easier