A differential equation is an equation that involves one or more derivatives of a function. It relates the function to its derivatives and specifies how the function changes over time.
The purpose of solving a differential equation is to find a function that satisfies the equation and describes the behavior of a system or process. This can help us make predictions and understand the underlying dynamics of a system.
The process of solving a basic differential equation involves isolating the dependent variable, finding its derivative, and then integrating both sides of the equation. This can be done using various methods such as separation of variables, substitution, and integration by parts.
Differential equations have a wide range of applications in various fields such as physics, engineering, economics, and biology. They are used to model and analyze systems and processes such as population growth, chemical reactions, electrical circuits, and motion of objects.
As a scientist, I am not able to check your specific work on solving a differential equation. However, there are many online resources and tools that can help you verify your solution and provide step-by-step explanations. It is also helpful to double-check your steps and calculations to ensure accuracy.