The Chain Rule & Implicit Differentiation · Superchallenge problem

A function $u(x,y) = \varphi\!\left(\dfrac{y}{x}\right)$, where $\varphi$ is a twice-differentiable function of one variable, is harmonic ($u_{xx} + u_{yy} = 0$) on the half-plane $x > 0$. If $\varphi(0) = 0$ and $\varphi(1) = 1$, find $\varphi(\sqrt3)$.