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Question: how to calculate the characteristic equation of differential equation in this Hermit case?

Question:how to calculate the characteristic equation of differential equation in this Hermit case?

Ex 95 Maple
diff
September 09 2012
0

sol := dsolve(t*diff(phi(x),x$2)-x*diff(phi(x),x)+n*phi(x),phi(x));
phi := unapply(rhs(sol), x);
BC := [phi(0)=0,phi(1)=0];
with(linalg):
Ccoef := genmatrix(BC, [_C1,_C2]);
CharEqn := det(Ccoef) = 0;

restart;
sol := dsolve(t*diff(phi(x,t,n),x$2)-x*diff(phi(x,t,n),x)+n*phi(x,t,n),phi(x,t,n));
phi := unapply(rhs(sol), x);
BC := [phi(0,0,0)=0,phi(1,1,1)=0];
with(linalg):
Ccoef := genmatrix(BC, [_C1,_C2]);
CharEqn := det(Ccoef) = 0;

i guess something wrong above, because result is zero
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