Boost converter: Finding conducting period for diode in DCM (theoretically)?
You wrote that no ripple is needed to take into the account. Then you simply calculate how long it takes until the loaded current of your inductor is diminished to zero when the voltage over the inductor is Vout-Vin. 

If your loaded current in the inductor is Ix then the needed time is Ix/((Vout-Vin)/L). You have actually tried this but got stucked with your solver machine.  At least Vin-Vout is different thing than Vout-Vin. Windows's calculator can be a better choice but try to swap the terms at first.

Things become complex if you take into the account the following factors:


Vout rises because the output capacitor gets charged
the load consumes part of the current, so all current from the L doesn't rise Vout


This is still an ideal case, but needs the differential equation or numerical simulation.