Find the solution to the below partial differential equation

d^2u/dx^2 =0

d^2u/dydx =0

d^2u/dy^2 =0

the ans is:

u(x,y) = Ax + By + C

when I did my working I got:

u(x,y)= Ax + g(y) where g(y) is an arbitary function.

I just want to know iff these 2 results are equivelent or my result is wrong?