$25$ points The set $of$ equations that satisfy the two$-$dimensional Poisson equation

$\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2}=f(x)$

$is$

$(a)u=x^2+y^2,f(x,y)=(x^2+y^2)$

$(b)u=x^3+y^3,f(x,y)=12(x+y)$

$(c)u=x^4+y^4,f(x,y)=12(x^2+y^2)$

$(d)u=x^4+y^4,f(x,y)=4(x^2+y^2)$