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Equilibrium solution limit to differential equation

Vishak

New member
Oct 27, 2013
18
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
Jan 26, 2012
1,403
Well what did you get for your solution?
 

Vishak

New member
Oct 27, 2013
18
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
Jan 26, 2012
1,403
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
Jan 26, 2012
4,193

Vishak

New member
Oct 27, 2013
18
Ok, thanks guys, I got the answer :)