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It means that the dependent variable and all its derivatives are multiplied by constants only, not by themselves nor by functions containing the independent variable..

For example, (dy/dx) + xy = 0 is non-linear

but (dy/dx) + y = (x^2)coswx is linear.

(Note that it doesnt matter how the function of the independent variable is)

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Q: What does it mean when a differential equation is linear?
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