This question looks really simple and thats whats worrying me a liittle.
Show that if f = f(x, y) and f_{yy}=0, then f(x, y) = g(x)y + h(x) for some funcions g, h.
I simply show that f_{yy} = 0 by differnetiation. Is That it ?
$\displaystyle \displaystyle \begin{align*} f_{yy} &= 0 \\ f_y &= \int{0\,dy} \\ f_y &= g(x) \textrm{ since partial differentiation of a function of x with respect to y gives 0} \\ f &= \int{g(x)\,dy} \\ f &= g(x)\,y + h(x) \end{align*}$