We classify all partial differential equations with polynomial coefficients in $chi$ and y of the form A($chi$) $u_{{chi}{chi}}$ ＋ 2B($chi$, y) $u_{{chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($chi$) $u_{{chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.