According to differential equations terms, one equation can be solved using quadrature if integration can be performed to obtain the desired solution, this applies well to separation of variables and certain substitution techniques, but integration is used also in finding integrating factors, and in Laplace transforms. i notice it's not used in solving the characteristic equation in linear ODES, also isn't numerical solutions aproximations to integrals?
A question rose, for what is a method of finding solutions of a differential equation that is not quadrature or that doesn rely on integration to yield a solution? what am i missing?