How do I transform a second-order PDE with constant coefficients into the canonical form? I tried to solve this problem: u_xx + 13u_yy + 14u_zz - 6u_xy + 6u_yz + 2u_xz -u_x +2u_y = 0 I wrote the bilinear form of the second order derivatives and diagonalized it. I found out that it is a hyperbolic equation. Now the problem is how to write it into the canonical form. What I tried is I wrote it as: u_aa + u_bb + u_cc + ...(first order derivatives) = 0 where a,b,c are the new variables (in which the matrix is diagonal) and computed the first order derivatives. Is this a good approach or something else should be done?