- #1
so , is my ans correct ?Simon Bridge said:That's already a first order differential equation.
hotjohn said:Homework Statement
dy/dx = (x +y) / (x-y) , i am asked to find the first order differential equation , but the ans i gt is different from the ans given
Homework Equations
The Attempt at a Solution
Simon Bridge said:That's already a first order differential equation.
hotjohn said:so , is my ans correct ?
A first order differential equation is a mathematical equation that involves an unknown function and its derivative with respect to an independent variable. It is called "first order" because the highest derivative in the equation is of the first order.
The main difference is that a first order differential equation involves only the first derivative of the unknown function, whereas a higher order differential equation involves derivatives of higher orders. This means that the solution to a first order differential equation will have only one arbitrary constant, while the solution to a higher order differential equation will have multiple arbitrary constants.
The general method for solving a first order differential equation is by separating variables, meaning that we isolate the dependent and independent variables on different sides of the equation. Then, we can integrate both sides to find the solution. Other methods include using substitution, exact equations, and integrating factors.
First order differential equations have various applications in fields such as physics, engineering, biology, and economics. They can be used to model growth and decay processes, population dynamics, electrical circuits, and chemical reactions, among many others.
No, not all first order differential equations have analytical solutions. Some equations may be too complex to solve using traditional methods, and numerical methods may have to be used instead. Additionally, some equations may have singular or non-continuous solutions, making it impossible to find a general analytical solution.