If I am asked to solve a differential equation "analytically", is this necessarily asking for explicit closed/open form solutions? Or are there other "analytical" techniques out there? ie: Would investigating solutions with phase diagrams count as an analytical technique?
For example: $$\dot{v}=v-\frac{v^3}{3}-w+a$$
$$\dot{w}=v+b-cw$$
where $a,b,c$ are real constants.
We can construct phase diagrams to analyse the trajectories for various parameter values, but we can't obtain explicit solutions for it.
The issue here is that I am not too sure if the term "analytically" is to be understood to be subjective, or if it has a very specific definition in the context of differential equations.