I have a system of three differential kinetic equations with three variables. I want to solve it using phase plain method. I know how to solve it in case of two variables, but don’t know what to do if there are 3 variables.
It can be solved finding isoclines, for each angle, for example if we have system
$$\dfrac{dx}{dt}=4x+3y$$
$$\dfrac{dy}{dt}=23+y$$
To find vertical isocline we need to do
$$\dfrac{23+y}{4x+3y}=tg(90^•)$$
We will get a formula, that describes an isocline line.
If have three equations with three variables, how to get isoclines?