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