Because you are dealing with state functions, the path doesn't matter. You can always get from initial (P1, V1, T1) to final (P2, V2, T2) state by a combination of a constant volume (or pressure) step and an isothermal step. For ideal gases, ΔU = 0 for the isothermal step. So for example

Constant vol: P1, V1, T1

P3, V1, T2 ΔU = C

_{v}ΔT

Isothermal: P3, V1, T2

P2, V2, T2 ΔU = 0

Constant pressure: P1, V1, T1

P1, V3, T2 ΔH = C

_{p}ΔT

Isothermal: P1, V3, T2

P2, V2, T2 ΔH = ΔU + Δ(PV) = 0