Solving Ordinary Differential Equations

We present a few rudimentary and general methods of solving first order linear and nonlinear differential equations which satisfy a specific form. We present general tests which can be run on the differential equations in question. If the equations satisfy the tests, the solutions to the differential equations can be written out directly. The analysis can be extended to a large class of differential equations, and can already tackle the general first order linear differential equation, the Bernoulli equation, separable differential equations, and a few differential equations we may be the first to solve.