difference between linear, semilinear and quasiliner PDE's

I think this will help you to understand the PDE $:$

Linear PDE: $a(x,y)u_x+b(x,y)u_y+c(x,y)u=f(x,y)$

Semi-linear PDE: $a(x,y)u_x+b(x,y)u_y=f(x,y,u)$

Quasi-linear PDE: $a(x,y,u)u_x+b(x,y,u)u_y=f(x,y,u)$

I hope these examples will help you.

Semilinear/Almost Linear PDE:

1) $a(x,y)u_x+b(x,y)u_y+c(x,y,u)=0$

2) $U_{tt}-U_{xx}+U^3=0$

Qausi Linear PDE:

1) $a(x,y,u)u_x+b(x,y,u)u_y-c(x,y,u)=0$

2) $U_x+UV_y=0$

3) $U_{tt}-UU_{xx}+U^3=0$

4) $U_{tt}-UU_{xx}+U=0$

5) Navier Stokes equation is also Qausi Linear Equation