First order differential equation

In summary, Simon is reminding hotjohn to state the problem clearly and use proper English, as well as avoiding posting images instead of typed equations. The given problem is already a first order differential equation and Simon is questioning if hotjohn's answer is correct.
  • #1
hotjohn
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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

 

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  • #2
That's already a first order differential equation.
 
  • #3
Simon Bridge said:
That's already a first order differential equation.
so , is my ans correct ?
 
  • #4
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 ?

hotjohn, I think Simon is indirectly chiding you for not following various forum rules, the first of which is to state the problem carefully. You asked "to find the first order differential equation" and Simon is pointing out that that is what you are given. You are also encouraged to use correct English, not expressions like "ans i gt". Finally, the worst thing is to post images instead of typed equations for your solution, making it impossible to edit your work if there are mistakes. Many of the homework helpers will not try to read or respond to such posts.
 
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1. What is a first order differential equation?

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.

2. What is the difference between a first order differential equation and a higher order differential equation?

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.

3. How do you solve a first order differential equation?

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.

4. What are some real-life applications of first order differential equations?

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.

5. Can all first order differential equations be solved analytically?

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.

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