differential equations at this level (ie odes that have tabulated solutions or are a transformation away from such an ode) are definitely a set of rules that yo

differential equations at this level (ie odes that have tabulated solutions or are a transformation away from such an ode) are definitely a set of rules that you memorize. differential equations as an active area of research is much more abstract, dealing with things like existence/uniqueness of solutions (when picard-lindelof doesn't apply), or stability when a solution is known to exist but cannot be analytically written down (and so integration has to be performed). hell one of the clay problems is about a solution to a pde. so no it's not this straightforward except in basically toy examples.