Help me - A function satisfies the differential equation

[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?

 

[Hootenanny]

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

 

[masqau]

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

 

[HallsofIvy]

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?

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.

 

[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

 

[Mark44]

i think it should be
y'(t)=t^4-6t^3+5t^2

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.

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