Question: diff(u(x,y),x,y)=x+y

eqs := [D[1, 2](u)(x, y) = x+y, u(x, 0) = x, u(0, y) = y]:

pdsolve(eqs[1], u(x, y));
                       u(x, y) = _F2(x)+_F1(y)+(1/2)*x^2*y+(1/2)*x*y^2

pdsolve(eqs[1 .. 2], u(x, y)); # indeterminate
                       u(x, y) = invfourier((y^2*undefined+signum(y)*infinity+y*(limit(-(2*I)*Pi*y/s1,
                       s1 = 0))+undefined)*Dirac(s1)+2*Pi*(limit((I*s1+y)/s1, s1 = 0))*Dirac(1, s1), s1, x)

pdsolve(eqs, u(x, y)); # doesn't satisfy the DE
                       u(x, y) = (Int(1, tau1 = 0 .. y)+1)*(-_F1(0)+x-_F2(0)+y)

(value@eval)(eqs, u = unapply(rhs(%), [x, y]));
                       [1 = x+y, -_F1(0)+x-_F2(0) = x, (y+1)*(-_F1(0)-_F2(0)+y) = y]

The first pdsolve is fine, but not the other two.