Producing a sinusoid from a DC input
I see the L-C tank and the voltage buffer, but there is no differentiator in your circuit.

It's hard to tell how you think this is supposed to work, but it's clearly not going to oscillate.  You will get some short-term ringing as Vin is changed, particularly when it is changed abruptly, but there is nothing to make this circuit oscillate.

A oscillator requires a total loop gain over 1 at some frequency but not at DC.  It should be obvious that this requirement hasn't been met since you don't have any loop at all.  Put another way, there is no feedback path, which is essential to a oscillator.