Your assertion doesn't make sense. Runge-Kutta does not solve differential equations. That's not what they are used for. A solution to a differential equation is an equation that satisfies both the differential equations and the boundary conditions. Runge-Kutta, or any other iterative numerical method, does nothing if the sort. The best they do is provide estimates on what values the solution might exhibit at a given point within their domain. These estimates may be of use for some application, but they are not solutions.

If you care about solutions to differential equations but for some reason don't want to learn methods that allow you to determine their solutions then the next best thing is getting up to speed with approximate methods such as the Galerkin method, which for some classes of problems and choices of trial functions can actually output exact analytical solutions.