# Help me - A function satisfies the differential equation

1. Feb 9, 2009

### butbi9x

A function satisfies the differential equation:

$$\frac{dy}{dt}= y^{4}-6y^{3}+5y^{2}$$

a. What are the constant solutions of the equation?
b. For what values of y is y increasing?
c. For what values of y is y decreasing?

2. Feb 9, 2009

### Hootenanny

Staff Emeritus
What are your thoughts on the problem? What have you attempted thus far?

3. Feb 20, 2010

### masqau

dy/dt=y'(t), its ur function or, simple, y(t), after integration.

Last edited: Feb 20, 2010
4. Feb 20, 2010

### HallsofIvy

Do you understand that this does NOT require that you actually solve the differential equation? It only requires that you solve an algebraic equation and two inequalities.

5. Feb 20, 2010

### masqau

i think it should be
y'(t)=t^4-6t^3+5t^2
where
y'(t)=dy/dt
now integrate it
we have
y(t)=........
constant solution mean y'(t)=0.
mean no variation w.r.t "t".
for what value of "t" is y increasing....
and for what value of "t" is y decreasing.
i think now u can handle it easily

Last edited: Feb 20, 2010
6. Feb 20, 2010

### Staff: Mentor

No, that's completely wrong. The DE equation is dy/dt = y4 - 6y3 + 5y2. If if were as you have it, this would be a different problem completely.