>Scheq := 1/2*h^2/Pi^2/mu*(diff(psi(xi,eta,phi),`$`(xi,2))*eta^2*xi^4-diff(psi(xi,eta,phi),`$`(eta,2))*eta^4*xi^2+2*diff(psi(xi,eta,phi),xi)*eta^2*xi^3-2*diff(psi(xi,eta,phi),eta)*eta^3*xi^2-2*diff(psi(xi,eta,phi),`$`(xi,2))*eta^2*xi^2-diff(psi(xi,eta,phi),`$`(xi,2))*xi^4+diff(psi(xi,eta,phi),`$`(eta,2))*eta^4+2*diff(psi(xi,eta,phi),`$`(eta,2))*eta^2*xi^2-2*diff(psi(xi,eta,phi),xi)*eta^2*xi-2*diff(psi(xi,eta,phi),xi)*xi^3+2*diff(psi(xi,eta,phi),eta)*eta^3+2*diff(psi(xi,eta,phi),eta)*eta*xi^2+diff(psi(xi,eta,phi),`$`(xi,2))*eta^2+2*diff(psi(xi,eta,phi),`$`(xi,2))*xi^2-2*diff(psi(xi,eta,phi),`$`(eta,2))*eta^2-diff(psi(xi,eta,phi),`$`(eta,2))*xi^2+diff(psi(xi,eta,phi),`$`(phi,2))*eta^2-diff(psi(xi,eta,phi),`$`(phi,2))*xi^2+2*diff(psi(xi,eta,phi),xi)*xi-2*diff(psi(xi,eta,phi),eta)*eta-diff(psi(xi,eta,phi),`$`(xi,2))+diff(psi(xi,eta,phi),`$`(eta,2)))/(eta^4*xi^2-eta^2*xi^4-eta^4+xi^4+eta^2-xi^2)/d^2-1/2*Z*e^2/Pi/epsilon[0]*psi(xi,eta,phi)/d/(eta+xi) = E*psi(xi,eta,phi);

Applying pdsolve to the above partial-differential equation yields three ordinary-differential equations, of which two are coupled, as follows.

> Xieq := diff(Xi(xi),`$`(xi,3)) = (-4*(xi-1)^2*((-1/4*xi^2+1/4)*diff(Xi(xi),xi)+Xi(xi)*xi)*h^2*(xi+1)^2*epsilon[0]*diff(Xi(xi),`$`(xi,2))+2*h^2*xi*epsilon[0]*(xi-1)^2*(xi+1)^2*diff(Xi(xi),xi)^2-2*Xi(xi)*h^2*epsilon[0]*(xi-1)^2*(xi+1)^2*diff(Xi(xi),xi)-4*Xi(xi)^2*(E*Pi^2*d^2*mu*xi^5*epsilon[0]+1/4*Pi*Z*d*e^2*mu*xi^4-2*E*Pi^2*d^2*mu*xi^3*epsilon[0]-1/2*Pi*Z*d*e^2*mu*xi^2+epsilon[0]*(1/2*m^2*h^2+E*Pi^2*d^2*mu)*xi+1/4*Pi*Z*d*e^2*mu))/h^2/Xi(xi)/epsilon[0]/(xi-1)^3/(xi+1)^3;

> Etaeq := diff(Eta(eta),`$`(eta,2)) = (h^2*Eta(eta)*epsilon[0]*(xi-1)^2*(xi+1)^2*(eta-1)*(eta+1)*diff(Xi(xi),`$`(xi,2))-2*h^2*Xi(xi)*eta*epsilon[0]*(xi-1)*(xi+1)*(eta-1)*(eta+1)*diff(Eta(eta),eta)-2*(-h^2*xi*epsilon[0]*(xi-1)*(xi+1)*(eta-1)*(eta+1)*diff(Xi(xi),xi)+((eta+xi)*(E*Pi^2*d^2*mu*(eta-1)*(eta+1)*xi^2-eta^2*E*Pi^2*mu*d^2+E*Pi^2*d^2*mu+1/2*m^2*h^2)*epsilon[0]+1/2*Pi*Z*d*e^2*mu*(xi-1)*(xi+1)*(eta-1)*(eta+1))*(eta-xi)*Xi(xi))*Eta(eta))/h^2/Xi(xi)/epsilon[0]/(xi-1)/(xi+1)/(eta-1)^2/(eta+1)^2;

> sol2 := dsolve({Etaeq,Xieq}, {Eta(eta),Xi(xi)});

>

With Maple 17 and before, this system of ordinary-differential equations that results from a partial-differential equation was solved with both 32- and 64-bit versions of Maple, but since then the 32-bit version produces either, after a few minutes, a hopelessly long and incorrect answer or just " { } ", whereas the 64-bit version produces a simple and presumably correct answer in a few seconds. This disparity should NEVER happen, but it continues to happen despite being notified to Maplesoft. How can we have confidence in further developments of partial-differential equations in Maple if this problem recurs and recurs and recurs in new release after new release after new release?