Put one predator in cages with different densities of prey and estimate prey mortality rate and corresponding k-value in each cage. As we know, k-value equals to the instantaneous mortality rate multiplied by time. However, the model can be modified to incorporate the relation of a to prey density. Now , parameters b and m can be taken from this regression equation.
Analytical methods are complicated and require good mathematical skills.
Also, many differential equations have no analytical solution at all. The simplest and least accurate is the Euler's method . The main source of error in the Euler's method is estimation of derivative at the start of time interval. However, the derivative at the center depends on the function value at the center which is unknown. Thus, first we need to estimate the function value at the middle point using simple Euler's method, and then we can estimate the derivative at the middle point.