No, that's impossible. If X is a trig function (and it must be for its derivative to be 0 at 0 and 1), then S must be negative: you must mean .

and now, because S is negative, -S is positive. so Y is exponential or hyperbolic: I would use Y(y)= C cosh(y)+ D sinh(y) because then Y(0)= C cosh(0)+ D sinh(0)+ C(1)+ D(0)= C= 0.X=cos(n pi x) n=0,1,2....

Y=Acos*square root of S * y + Bsin* square root of S * y

since Y(0)=0

so Y=Bsin(n pi y)

so X(x)Y(y)=Bcos(n pi x)* sin(n pi y)

i know it's not finished, but is it correct from here? cos i dont feel quite sure about it....thank you~