Consider the predator prey model and make change of variables to put it in dimensionless form. I have this predator-prey model \begin{align*} \frac{dH}{dt} &= rH \left(1-\frac{H}{K} \right) - \alpha \frac{PH}{H+ \beta} \\\ \frac{dP}{dt} &= \gamma P \left( -1+ \delta \frac{H}{H+ \beta} \right) \end{align*} And I am asked to make the following change of variables to put the model in dimensionless form. $$x=\frac{H}{K}, \ \ y=\frac{\alpha}{rK}P, \ \ \text{and} \ \ \tau=rt.$$ Then \begin{align*} \frac{dx}{d \tau} &= x \left(1-x-\frac{y}{x+b} \right) \\\ \frac{dy}{d \tau} &= cy \left(-1+a\frac{x}{x+b} \right) \end{align*} Can someone give me a HINT

This is very easy. It's just replacing of variables and constants by new variables and constants, and the chain rule, of course. For example, $${dx\over d\tau}={1\over K}\>{dH\over d\tau}={1\over K}\>{dH/dt\over d\tau/dt}={1\over Kr}\>{dH\over dt}=\ldots\quad.$$ Now plug in the right side from your first equation, and express everything in terms of the new variables/constants. Same thing with the second equation.