# ap.analysis of pdes – eliminating first derivative terms from second order elliptic partial differential equation

I have a partial differential equation
$$-afrac{partial^2 G}{partial x_1 partial x_2}-b(cosh(x_1)+cosh(x_2))G(x_1,x_2)+sinh(x_1)frac{partial G(x_1,x_2)}{partial x_1}+sinh(x_2)frac{partial G(x_1,x_2)}{partial x_2}=epsilon ,,G(x_1,x_2)$$

I have to cast it in a form like
$$-frac{1}{m_1}frac{partial^2 psi}{partial x^2}-frac{1}{m_2}frac{partial^2 psi}{partial y^2}+U(x,y),psi=epsilon ,,psi$$

for some variable transformation from {$$x_1,x_2rightarrow x,y$$} and also some transformation in $$G(x,y)$$. How to do this?