The second-order differential equation in an unknown function $u: u(x, y)$ is defined as
\[
\frac{\partial^{2} u}{\partial x^{2}}=2
\]
Assuming $g: g(x), f: f(y)$, and $h: h(y)$, the general solution of the above differential equation is
- $u=x^{2}+f(y)+g(x)$
- $u=x^{2}+x f(y)+h(y)$
- $u=x^{2}+x f(y)+g(x)$
- $u=x^{2}+f(y)+y g(x)$