## Linearity

I'm trying to see if $$\rho$$utt + EIuxxxx = 0 is linear or non-linear where $$\rho$$, E and I are constants.

I got L(u+v) = $$\rho$$$$\delta$$2u2/$$\delta$$t2 + EI$$\delta$$4u2/$$\delta$$x4 + $$\rho$$$$\delta$$2uv/$$\delta$$t2 + EI$$\delta$$4uv/$$\delta$$x4 = Lu + Lv. Does this mean it's linear or is there more to do.

 PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target
 Recognitions: Gold Member Homework Help Science Advisor That is enough.
 Cheers. What about this one then. ut - $$\alpha^2$$$$\nabla^2$$u = ru(M -u) where $$\alpha$$, r & M are constants. ut - $$\alpha^2$$$$\nabla^2$$u - ru(M -u) = 0 L(u+v+w) = ut(u+v+w) + $$\alpha^2$$$$\nabla^2$$u(u+v+w) - ru(M-u)(u+v+w) = utt + $$\alpha^2$$$$\nabla^2$$u2 - ru2(M-u) + utv + $$\alpha^2$$$$\nabla^2$$uv - ruv(M-u) + utw + $$\alpha^2$$$$\nabla^2$$uw - ruw(M-u) = Lu + Lv + Lw

## Linearity

Are these equation linear or non-linear?

ut + (1-u)ux = 0
uxx + exutt = sin(x)
uxx + uxy + uyy + ux = t2