Your above calculation is fine. However, if the question is about a system where we don't have an expression for the internal energy, U, then I think we are stuck. The first answer suggested that one use dU= cv dT. My reply was that the internal energy can be a function of volume, and I...
I don't think that your hint will actually work. In the derivation you cite, they use a relationship:
dU = n\, c_v\, dT
For the ideal gas, the internal energy is only a function of the temperature, so the above relationship holds for all processes, not only constant volume ones...