You can do quite a lot simplifying to get equations that are solvable. A lot of engineering techniques do this, using simplifications that capture the essential behavior of a system (in fact I'd argue that knowing when such approximations are appropriate is one of the core skills of an engineer).
That said, even if you need a numerical solution it will still often require a lot of simplifications in order to be tractable. Multiphase fluid flow, for instance, relies on tons of physics simplifications and empirical correlations in order to make numerical techniques viable.
That said, even if you need a numerical solution it will still often require a lot of simplifications in order to be tractable. Multiphase fluid flow, for instance, relies on tons of physics simplifications and empirical correlations in order to make numerical techniques viable.