In general, the use of numerical methods to solve systems of differential equations is necessary when carrying out the analytical solution is very difficult.
There are several programs where systems of differential equations (ODE) can be solved numerically, for example, the most famous one is MATLAB. In this program you can use the "ODE Solver" tool to solve ODE systems.
Assuming you talk about the reaction kinetics of transesterification of vegetable oil with methanol or ethanol, ODE15S is the best option since these equations are stiff. On the internet there is a lot of information on how to solve these systems through MATLAB or other programs, for example, the following link can be very helpful : https://www.mathworks.com/videos/solving-odes-in-matlab-7-stiffness-ode23s-ode15s-117651.html