Consider a water tank shown in the figure. It has one wall at $x = L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$, the liquid surface makes angle $\theta_0\ (\theta_0 \ll 1)$ with the $x$-axis at $x = L$. If $y(x)$ is the height of the surface, then the equation for $y(x)$ is: (take $\theta(x) = \sin\theta(x) = \tan\theta(x) = \frac{dy}{dx}$, $g$ is the acceleration due to gravity)
Balancing the Laplace pressure of the curved surface, $S\,\dfrac{d^2y}{dx^2} = \rho g\,y$ for small slopes, i.e. $\dfrac{d^2y}{dx^2} = \dfrac{\rho g}{S}\,y$.