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October 27th, 2017, 02:59 AM   #1
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linear or non-linear

May I know the reason why the differential equation:

|dy/dx| = y is non-linear differential equation?
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October 27th, 2017, 03:25 AM   #2
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It is non linear because taking the modulus of the derivative (or anything else) is a non linear process.
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October 27th, 2017, 05:08 AM   #3
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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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