Calculating Delta H for Non Ideal Gasses We have to calculate delta H for a gas that follows the Van der Waals equation of state: 

$$\left(p + \frac{a}{V_\mathrm m^2}\right)\left(V_\mathrm m-b\right)=RT$$

I know that $H = U + pV$ but I don't know how to approach this question.

Since I also know that $\Delta H = \Delta U + \Delta (pV)$, does that mean that I can calculate this simply by calculating $\Delta U$ (which I know how to do) and then $\Delta (pV) = p_2V_2 - p_1V_1$? Is that an appropriate method?

Because previously in other questions I have also seen it done as
$\mathrm{d}H = \mathrm{d}U + V\mathrm{d}p + p\mathrm{d}V + \mathrm{d}V\mathrm{d}p$ so I am wondering when is which equation applicable?
Are you familiar with the following equation?:  $$dH=C_pdT+\left(V_m-T\left(\frac{\partial V_m}{\partial T}\right)_P\right)dP$$