Differential transformation method can be used to solve differential equation even integro-differential equations.

Differential transformation is a method that applies the Taylor expansion of the function. For an arbitrary function $f(x)$, we can Taylor expand it

$$$$f(x) = \sum_{n=0}^N F(n) (x-x_0)^n,$$$$

where $F(n)$ is the coefficient of Taylor expansion. By using the definition, we can explore the properties of this transformation from function $f(x)$ to $F(n)$.