)A first order differential equation is a mathematical equation that involves an unknown function and its derivative (or rate of change). It is called "first order" because it only involves the first derivative of the function.
To solve a first order differential equation, you need to find the function that satisfies the equation. This can be done using various techniques such as separation of variables, integrating factors, or using specific formulas for certain types of equations.
An ordinary differential equation involves a single independent variable, while a partial differential equation involves multiple independent variables. This means that the solution to a partial differential equation is a function of more than one variable.
No, it is not possible to find a unique solution to a first order differential equation without knowing the initial conditions. These initial conditions provide the starting point for finding the solution, and without them, the solution would be a general solution rather than a specific one.
First order differential equations are used in many fields of science, including physics, chemistry, biology, and engineering. They are used to model and describe various physical phenomena, such as the growth of populations, the decay of radioactive substances, and the motion of objects under the influence of forces.