
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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October 27th, 2017, 01:59 AM  #1 
Member Joined: Apr 2017 From: India Posts: 34 Thanks: 0  linear or nonlinear
May I know the reason why the differential equation: dy/dx = y is nonlinear differential equation? 
October 27th, 2017, 02:25 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 845 Thanks: 253 
It is non linear because taking the modulus of the derivative (or anything else) is a non linear process.

October 27th, 2017, 04:08 AM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 417 Thanks: 231 Math Focus: Dynamical systems, analytic function theory, numerics 
To illustrate what studiot is saying: Linear functions satisfy $f(x + y) = f(x) + f(y)$. If you take $x = 3,y=3$ its easy to see that $\cdot$ is not linear. A differential equation is nonlinear if it is a nonlinear equation with respect to any of $y,y',y'',\dots$. In other words, if the solution or any of its derivatives are nonlinear in the equation, then the DE is nonlinear. 

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linear, lineasr, nonlinear 
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