The statement is True.

A differential equation (DE) is considered exact if there exists a function $\psi(x, y)$ such that the equation can be written in the form of a total differential:

$M(x, y) dx + N(x, y) dy = 0$

where $M(x, y)$ and $N(x, y)$ are the components of the equation. If the equation is exact, it means there is a potential function $\psi(x, y)$ such that:

$\frac{\partial \psi}{\partial x} = M(x, y) \quad \text{and} \quad \frac{\partial \psi}{\partial y} = N(x, y)$

This implies that a solution can indeed be found that satisfies the equation exactly, without the need for approximation.

Would you like further details or clarification on exact differential equations?

Here are 5 follow-up questions you may find interesting:

1. How do we check if a differential equation is exact?
2. What is the method for solving exact differential equations?
3. What are some examples of exact differential equations?
4. What happens if a differential equation is not exact?
5. Can an inexact differential equation be made exact, and how?

Tip: Always check for the condition $\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$ to determine if a differential equation is exact!