This paper is concerned with distributed order differential equations which arise as a generalisation of fractional differential equations when the order of the derivative is allowed to vary in the equation. The paper is structured as follows: after the necessary mathematical background is described, the authors show how a distributed order differential equation may be re-expressed as a distributed order integral equation. Next the authors generate a generalised Taylor series expansion for the solution. The Laplace transform approach that is classically used to solve fractional differential equations can be applied to the Taylor series. Now the authors show an alternative (nonstandard) approach for generating the inverse Laplace transform. They present an example that shows that the various approaches can lead to the same solution.