Problem analyzing diode circuit
By inspection, V1 and V2 in their shown position and polarity both will create a current flow through D1 and D2 will become reverse biased. This could have been different if R1 was 10 kohm and R2 was 5 kohm.

In other words, use your eyes and have a think before launching into a theorem that might not work with non-linear components.

So, now you know which "ideal" diode is conducting and which "ideal" diode isn't, throw them away and replace with either a short (conducting) or an open (non-conducting).

This leaves a very simple arrangement: -



Can you take it from here?