# Equilibrium solution limit to differential equation

#### Vishak

##### New member
Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next.

Consider dx/dt = x^3 - 4x

Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t).

Thanks!

#### Prove It

##### Well-known member
MHB Math Helper
Well what did you get for your solution?

#### Vishak

##### New member
Well what did you get for your solution?
I got the equilibrium solutions x = -2 , 2 and 0. Out out these only x = 0 is stable. Not sure where to go from here though...

#### Prove It

##### Well-known member
MHB Math Helper
I meant, what did you get for your solution to the DE? Hint: It's separable and can be solved using Partial Fractions.

#### Ackbach

##### Indicium Physicus
Staff member
I meant, what did you get for your solution to the DE? Hint: It's separable and can be solved using Partial Fractions.
It's also Bernoulli, as an alternative.

#### Vishak

##### New member
Ok, thanks guys, I got the answer