# Thread: Another question

1. ## Another question

I'm stuck on another problem that asks me to find constant solutions to the equation $\frac{dy}{dt}=y^4-6y^3+5y^2$ and to determine when y increases/decreases.

I've integrated and I've got $y=\frac{y^3}{3}-\frac{3}{2}y^4+\frac{5}{3}y^3$ and then I thought about doing algebra to solve for y but that wouldn't work.

2. Originally Posted by superdude
Thanks, what I'm doing now makes sense.
I'm stuck on another problem that asks me to find constant solutions to the equation $\frac{dy}{dt}=y^4-6y^3+5y^2$ and to determine when y increases/decreases.

I've integrated and I've got $y=\frac{y^3}{3}-\frac{3}{2}y^4+\frac{5}{3}y^3$ and then I thought about doing algebra to solve for y but that wouldn't work.
When the fucntion is decreasing, $\frac{dy}{dx}$ is negative, when its increasing: $\frac{dy}{dx}$ is positive.

So,
Find the roots of:
$\frac{dy}{dt}=y^4-6y^3+5y^2$

I'll start you off here:

$
0 = y^2(y^2-6y+5)
$

Plug the roots in to the original DE, then take one number less than the root and one number more than the root and plug it in as well. See what kind of result you get.