Is there a general theory for linear, 2nd-order PDE in two dimension, when all coefficients are linear functions of the two variables?
If not, how would you proceed with an equation like
$$ x f_{xx} + (k_1+k_2 x) f_x + ( k_3 + k_4 x +k_5 y ) f_y + k_6 f = 0$$
Thank you.