Diode circuit question. Got answer but not sure about nodal analysis
No, you can't just assume both diodes will be on.  You have to decide that first as it will impact the rest of the analisys.  Start by ignoring D1 and then see if its anode voltage would be high enough to turn it on.  Then you proceed with one of two branches in analyzing the circuit, depending on whether D1 is on or not.

When D1 is on, then its anode will be one diode voltage above ground.  You then assume D2 drops the same voltage, so that its cathode is also at ground.  Now you have all the voltages in the circuit, so you can find the currents by Ohm's Law.

When D1 is off, then just cross it off and pretend it's not there.  Now you just have two resistors and a diode in series.  Figure the diode looks like a voltage source of one diode drop, and the rest is just a resistor divider.

By the way, you should be able to tell from inspection whether D1 is conducting or not, but do the math if you're not sure.