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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 October 27th, 2017, 02:59 AM #1 Member   Joined: Apr 2017 From: India Posts: 34 Thanks: 0 linear or non-linear May I know the reason why the differential equation: |dy/dx| = y is non-linear differential equation?
 October 27th, 2017, 03:25 AM #2 Senior Member   Joined: Jun 2015 From: England Posts: 891 Thanks: 269 It is non linear because taking the modulus of the derivative (or anything else) is a non linear process.
 October 27th, 2017, 05:08 AM #3 Senior Member   Joined: Sep 2016 From: USA Posts: 502 Thanks: 280 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. Thanks from studiot and shashank dwivedi

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