The difference between linear and non linear differential equation

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SUMMARY

The discussion clarifies the distinction between linear and non-linear differential equations. A linear differential equation does not include non-linear functions of the dependent variable, while non-linear equations do. The linear function is defined as f(x) = ax + b, where 'a' and 'b' can be functions of other variables but must maintain linearity in 'x'. Understanding this difference is crucial for solving ordinary differential equations effectively.

PREREQUISITES
  • Basic understanding of ordinary differential equations
  • Familiarity with linear functions and their properties
  • Knowledge of dependent and independent variables in mathematical contexts
  • Ability to identify non-linear functions
NEXT STEPS
  • Study the characteristics of linear differential equations
  • Explore methods for solving non-linear differential equations
  • Learn about the applications of linear and non-linear differential equations in real-world scenarios
  • Review examples of both types of equations to solidify understanding
USEFUL FOR

Students and educators in mathematics, particularly those focusing on differential equations, as well as anyone interested in the foundational concepts of linear versus non-linear functions.

fabianz
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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:
 
Last edited:
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its pretty much the difference between ones you can solve and ones you cannot.
 
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
 

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