Is \rhoutt + EIuxxxx = 0 a Linear or Non-Linear Math Problem?

[squenshl]

I'm trying to see if $$\rho$$u_tt + EIu_xxxx = 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.

 

[arildno]

That is enough.

 

[squenshl]

Cheers.
What about this one then.
u_t - $$\alpha^2$$$$\nabla^2$$u = ru(M -u) where $$\alpha$$, r & M are constants.

u_t - $$\alpha^2$$$$\nabla^2$$u - ru(M -u) = 0
L(u+v+w) = u_t(u+v+w) + $$\alpha^2$$$$\nabla^2$$u(u+v+w) - ru(M-u)(u+v+w) = u_tt + $$\alpha^2$$$$\nabla^2$$u² - ru²(M-u) + u_tv + $$\alpha^2$$$$\nabla^2$$uv - ruv(M-u) + u_tw + $$\alpha^2$$$$\nabla^2$$uw - ruw(M-u) = Lu + Lv + Lw

 

[squenshl]

Are these equation linear or non-linear?

u_t + (1-u)u_x = 0
u_xx + e^xu_tt = sin(x)
u_xx + u_xy + u_yy + u_x = t²

 

[squenshl]

Someone help please.