I've got the following differential equation: $$\frac{dx}{dt}=rx(k-x) \quad \quad x(0)=x_0$$ I have to perform several changes of parameters/variables so that instead of depending on $x, k, x_0$ the differential equation depends on one parameter only. I've tried $$y=\frac{x}{k} \quad \quad \tau=rt$$ and this way my equation is (where $\dot{y}=\frac{dy}{d\tau}$): $$\dot{y}=\frac{1}{k}y(1-y) \quad \quad y(0)=\frac{x_0}{k}$$ Here I still have two parameters $(k,x_0)$ and I should have only one. Can someone help me continue?
Edit: Just to clarify, my final equation should depend on one parameter and of course it will also depend on the variable