Is there any method to solve differential equations which involves just a number of basic functions combined into various permutations (with various factors) which are then fed into the differential equations, which would leave, in the ideal case, just an equation of the various factors to solve?
Obviously it would not work for quite a lot of differential equations but I tend to notice that a large number of common differential equations tend to be just a rather small combination of various simple functions, and I am wondering if such a method already exists or if it could work to some degree.