A 1st order ODE, or first order ordinary differential equation, is a mathematical equation that involves an unknown function and its derivative with respect to a single independent variable.
The process for solving a 1st order ODE involves finding an expression for the unknown function that satisfies the given differential equation. This is typically done through various methods, such as separation of variables, integrating factors, or using a substitution.
1st order ODEs are used in a variety of scientific fields, including physics, engineering, and economics. They can be used to model various physical systems, such as the motion of objects or the growth of populations.
The initial conditions for solving a 1st order ODE are the values of the unknown function and its derivative at a specific point. These conditions are typically given in the problem and are used to determine the specific solution to the differential equation.
Some common techniques for solving 1st order ODEs include separation of variables, integrating factors, and substitution. Other techniques, such as the use of Laplace transforms or power series, may also be used for more complex equations.