# Definition:Differential Equation/Solution Set

< Definition:Differential Equation(Redirected from Definition:General Solution)

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## Contents

## Definition

Let $\Phi$ be a differential equation.

The **solution set** (or **the solution**) of $\Phi$ is the set of *all* functions $\phi$ that satisfy $\Phi$.

## Also known as

The **solution set** of a differential equation $\Phi$ can also be referred to as **the solution** of $\Phi$, but beware of confusing this with the concept of **a solution** of $\Phi$.

The **solution set of a differential equation** can also be referred to as a **solution set to a differential equation**.

The term **general solution** is also frequently encountered.

## Also see

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.2$: General Remarks on Solutions - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**differential equation**