The difference between linear and non linear differential equation

In summary, Linear and nonlinear differential equations differ in their ability to be solved. A linear differential equation can be solved if it is in the form of f(x) = ax + b, while a nonlinear equation involves more complicated functions. In other words, a linear equation is simpler and more manageable, while a nonlinear equation is more complex and may require more advanced techniques to solve.
  • #1
fabianz
1
0
I'm just starting to learn about ordinary differential equation and I'm still
don't know how to find the difference between linear and non linear differential equation.
I'm really confused about it, even after I'm reading my textbook:confused:.
Would someone help me please?
thank you very much:smile:
 
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  • #2
its pretty much the difference between ones you can solve and ones you cannot.
 
  • #3
Oh, now that's just silly! (Though pretty much true!)

fabianz, do you know the difference between linear and nonlinear functions?

A linear function must be of theform f(x)= ax+ b. Nothing more complicated than multiplying by a number and adding a number. For a function of several variables, "a" and "b" can be any function of the other variables and still be "linear in x". Any thing other than that is "non-linear".

A differential equation if "linear" if it does not involve any non-linear functions of the dependent variable
 

1. What is the main difference between linear and non-linear differential equations?

The main difference between linear and non-linear differential equations is the presence of the dependent variable in the equation. In linear differential equations, the dependent variable and its derivatives appear only in a linear form, while in non-linear differential equations, they can appear in any form (e.g. exponential, logarithmic, trigonometric).

2. Can you give an example of a linear differential equation?

One example of a linear differential equation is the first-order linear equation: dy/dx = x + y. This equation can be easily solved using integration and the solution will be a straight line.

3. How do you solve a non-linear differential equation?

The solution to a non-linear differential equation is not as straightforward as a linear one. It often involves using numerical methods or making certain substitutions to transform the equation into a linear form. In some cases, there may not be an exact solution and approximations must be made.

4. What are some real-life applications of linear and non-linear differential equations?

Linear differential equations are commonly used in physics and engineering to model simple systems such as motion and electrical circuits. Non-linear differential equations are often used to model more complex systems, such as population growth and chemical reactions.

5. How do you know if a differential equation is linear or non-linear?

You can determine if a differential equation is linear or non-linear by looking at the form of the equation. If the dependent variable and its derivatives appear in a linear form, it is a linear differential equation. If they appear in any other form, it is a non-linear differential equation.

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