Char. Limit said:First rearrange it to dy/dx + p(x) y = q(x), where p(x) and q(x) are arbitrary functions. Then find an integrating factor.
A first order differential equation is an equation that involves a function and its derivative. It is called first order because it only involves the first derivative of the function.
The most common method for solving a first order differential equation is by using separation of variables. This involves isolating the dependent variable and its derivative on opposite sides of the equation, and then integrating both sides.
First order differential equations are used to model a variety of real-world problems in fields such as physics, engineering, and economics. Solving these equations allows us to predict and understand the behavior of systems over time.
No, not all first order differential equations can be solved analytically. Some equations may require numerical methods or approximations to find a solution.
First order differential equations are commonly used in physics to model motion and in engineering to analyze circuits. They are also used in biology to describe population growth and in economics to model supply and demand.