# Determining the equation of state when given thermodynamic relations [closed]

Empirical observations of a thermodynamic system have shown that:

\begin{align}C_{\mathrm m,V} &\neq C_{\mathrm m,V}(T) \\[6pt] \left(\frac{\partial U}{\partial V_\mathrm m}\right)_{T} &= f(V_\mathrm m) \\[6pt] \left(\frac{\partial U}{\partial p}\right)_{V} &= g(V_\mathrm m) \end{align}

where $f$ and $g$ are functions of the molar volume, $V_\mathrm m$. Determine the state equation.

How can I solve this problem?