# Solution of the equation $y^{\prime}=f(y)$ and Bell Polynomials

## TL;DR

This paper employs Bell polynomials and Faa di Bruno's formula to solve differential equations of the form y' = f(y), providing a novel approach to express solutions and compute Bell polynomial values.

## Contribution

It introduces a method linking Bell polynomials with differential equations, enabling explicit solution representation and computation of Bell polynomial values.

## Key findings

- Derived explicit solutions using Bell polynomials
- Connected Bell polynomial values to differential equation solutions
- Provided a new computational approach for Bell polynomials

## Abstract

In this paper we use Faa di Bruno's formula to associate Bell polynomial values to differential equations of the form $y^{\prime}=f(y)$. That is, we use partial Bell polynomials to represent the solution of such an equation and use the solution to compute special values of partial Bell polynomials.