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## Homework Statement

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

## Homework Equations

L is a linear operator if:

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

## 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