- #1
Noesis
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I'm just curious as to what the actual distinction means.
I understand that the requirement for a linear ODE, is for all the coefficients to be functions of x (independent variable), and that all derivatives or y's (dependent variable) must be of degree one, but that doesn't tell me much.
In a normal function, there is a clear distinction between a linear and a nonlinear one.
For example, y = 3x, it's clear here that y changes linearly with x, and is always three times as big as x.
On y = x^2, it's obvious that the change is not linear...so the relationship isn't linear.
Now how can I analyze linear differential equations and nonlinear differential equations in a similar manner?
How does their behavior, or their 'meaning' differ?
I understand that the requirement for a linear ODE, is for all the coefficients to be functions of x (independent variable), and that all derivatives or y's (dependent variable) must be of degree one, but that doesn't tell me much.
In a normal function, there is a clear distinction between a linear and a nonlinear one.
For example, y = 3x, it's clear here that y changes linearly with x, and is always three times as big as x.
On y = x^2, it's obvious that the change is not linear...so the relationship isn't linear.
Now how can I analyze linear differential equations and nonlinear differential equations in a similar manner?
How does their behavior, or their 'meaning' differ?