(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

L is a linear operator if:

cL(u)=L(cu) and L(u+v)=L(u)+L(v)

3. The attempt at a solution

L = d/dt + d^2/dx^2 + 1

L(cu) = d(cu)/dt + d^2(cu)/dx^2 + 1 = c du/dt + c d^2(u)/dx^2 + 1 ≠ cL(u) = c du/dt + c d^2/dx^2 + c. So I found that it is not linear since it does not satisfy cL(u)=L(cu). However the solution tells me that it is. Can anyone spot my error?

Thanks

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# Homework Help: Check PDE for linearity

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