How to approach diode circuit analysis (novice)
Here's your circuit, redrawn a bit with more labels.







simulate this circuit &ndash; Schematic created using CircuitLab

You can determine the state of the diodes without any math, just reasoning about the circuit. In these situations I find it helpful to imagine that there's no voltage across any of the resistors (through some magic mechanism), and then consider how the circuit will behave as it approaches equilibrium.

Initially the voltage across R2 is 0, so D1 and D2 are forward. This permits more current to flow through R2, pushing up nodes B and C with it.

Once C is at 0V, both diodes are forward, but only just. If C creeps above 0V, D1 will be reverse biased.

Will it? I can see that R1 and R2 make a voltage divider, and the voltage across R2 must be twice that of R1. With C at 0V, that's not the case: we have 10V across R1 and 9.3V across R2.

So the voltage at C will continue to rise, and D1 will be reverse biased. The voltage at C will continue rising until the voltage divider is in equilibrium, and D2 will remain forward biased.