Classify the equations in terms of order, linearity, homogeneity, and for second order equations classify as elliptic, hyperbolic, or parabolic.

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  1. $u_x+3u_t=u$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  2. $(u_{xy})^2=u$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  3. $u_{t}+u_{xx}=u$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  4. $u_{xx}+u^2 - u_{yy} = 0$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  5. $u^2u_t+u_x+u_y=xy$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  6. $u_{xx}+u_{yy}=0$

? Second order, linear, homogeneous, elliptic Second order, linear, homogeneous, hyperbolic Second order, linear, homogeneous, parabolic Second order, linear, nonhomogeneous, elliptic Second order, linear, nonhomogeneous, hyperbolic Second order, linear, nonhomogeneous, parabolic Second order, nonlinear First order, linear, homogeneous First order, linear, nonhomogeneous First order, nonlinear  7. $u_{xx}=u_{tt}+u_x+u+xt$