Classify the as elliptic, hyperbolic, or parabolic as long as they are of second order. (correct answer is not shown until you get all of them right)

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  1. $u_{xx}+u_{xy}-u_{yy}=0$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  2. $u_{x}+xu_{y}=\sin(x)$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  3. $u_{xx}+y^2 u_{xy}-3u_{yy}+10u_y=u$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  4. $u_{xx}+(x^2+y^2)u_{xy}+u_{yy}=u$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  5. $u_{xx}+xu_{yy}+10u_y=u_{xxx}$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  6. $u_{xx}+u_{xy}-(x^2)u_{yy}+10u_x=x^2+y^2$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  7. $u_{xy}+xu_{yy}+yu_y=xu$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  8. $u_{xx}+u_{xy}+3u_{yy}=0$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  9. $u_{xx}-u_{xy}+3u_{yy}+10u_y=u$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  10. $u_{xx}+u_{xy}+3u_{yy}+10u_x=x^2+y^2$

? elliptic parabolic hyperbolic not second order somewhere elliptic somewhere hyperbolic  11. $u_{xx}+xu_{yy}+10u_y=u$