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A differential equation is a mathematical equation that relates a function with one or more of its derivatives. It describes how a quantity changes over time or in relation to other variables.
The purpose of solving a differential equation is to find the function that satisfies the equation. This function can then be used to model and predict the behavior of a system in various scenarios.
The steps for solving a differential equation include: identifying the type of equation, separating variables, integrating both sides, applying boundary conditions, and simplifying the solution to get the final answer.
A solution to a differential equation is correct if it satisfies the given equation and any specified boundary conditions. It should also be a continuous and differentiable function.
Differential equations are used in many fields of science and engineering, such as physics, chemistry, biology, economics, and engineering. They are particularly useful in modeling and predicting the behavior of systems, such as population growth, chemical reactions, and electrical circuits.