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10Hz to 10Mhz is a wide frequency range, it would be very hard to cover that whole range in the analogue domain, as you have discovered analogue oscillators that can span more than a factor of about 3 frequency are tricky. so far as I know the best perfoming tunable oscillator is the Vackář_oscillator.

But you're asking for 1:100000 range, in a simple oscillator that's not going to happen.

Early television sets used one oscillator for each channel, switching channels with a clunky channel selector that swapped the inductors and capacitors in the circuit, later designs mangaed a 1:3 tuning range and split the frequency range into 3 parts,  approximately ( 45-115 , 115-300 and 300-900 )

for a 1:100000 range The only analogue approach that I can see working would be to make a higher frequency say 10.7MHz to 11.7MHz using some sort of tuned circuit and then "mix it down" by multiplying it with a fixed 10.7MHz  perhaps using a Gilbert cell, and then a low pass filter to exclude the original signals and the upper sideband. (10.7 MHz chosen because it's used in FM radio receivers, so filters etc should be readily available)

Others have suggested using AD9850 which is a digital chip that uses DDS to produce a sine wave,  this seems a far easier approach, copy the example design from the datasheet, or purchase a pre-assembled module.

If you don't want to learn all about radio design from the last century the DDS is the right approach.