How do you solve a first-order differential equation?

Problem Statement

How do you solve a first-order differential equation?

Step-by-Step Explanation

First-order differential equations often use separation, integrating factors, or direct integration.

1. Identify what the question is asking. In Differential Equations, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

First-order differential equations often use separation, integrating factors, or direct integration. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.