# Having trouble solving this separable differential equation I am having some trouble with the following separable differential equation (dx)/(dt) = x(x-1)(x-3) with initial condition x(0)=2. What is lim_(t -> oo) x(t) I am having some trouble with the logarithmic laws when solving for x(t).

Having trouble solving this separable differential equation
I am having some trouble with the following separable differential equation
$\frac{dx}{dt}=x\left(x-1\right)\left(x-3\right)$
with initial condition $x\left(0\right)=2$. What is $\underset{t\to \mathrm{\infty }}{lim}x\left(t\right)$?
I am having some trouble with the logarithmic laws when solving for $x\left(t\right)$
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encoplemt5
You do not have to solve the differential equation
$\frac{dx}{dt}=x\left(x-1\right)\left(x-3\right)$
Note that you have three equilibrium points, namely
$x=0,1,3$
Qualitative analysis of these equilibrium points show that $x=1$ is asymptotically stable.
Thus starting at $x\left(0\right)=2$ the solution will tend to $x=1.$