The difference between linear and non linear differential equation

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Linear differential equations are characterized by their ability to be expressed in a specific form, typically involving only linear combinations of the dependent variable and its derivatives. In contrast, non-linear differential equations include non-linear functions of the dependent variable, making them more complex and often harder to solve. The distinction primarily lies in the solvability of these equations, with linear equations generally being easier to solve than their non-linear counterparts. Understanding this difference is crucial for students learning ordinary differential equations. Mastery of these concepts is essential for progressing in differential equations studies.
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:
 
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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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