These 2 questions are somewhat related:(adsbygoogle = window.adsbygoogle || []).push({});

Is the operator linear: Lu = du/dx + du/dy + 1

I said it's non-linear since L(u+v) = du/dx + dv/dx + du/dy + dv/dy + 1 = Lu + Lv - 1 =/= Lu + Lv

and then:

State whether each of the following equations is nonlinear, linear inhomogeneous, or linear homogeneous.

du/dt - d^2u/dx^2 + 1 = 0

which can be rewritten as du/dt - d^2u/dx^2 = -1

so now we have pretty much the same situation as above, except since it was set to zero, i can just bring the 1 on the other side and the resulting equation is linear and non-homogeneous Lu = -1

So then, is my reasoning for the first question wrong, that the operator (which is almost identical except for the order of derivatives) is actually linear? And then, why is my reasoning wrong?

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# Homework Help: Simple linear(?) operator

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