I am having difficulties on how to start the design.
Could you please guide me through this?

 

Goto DigiKey.com. Do a parametric search for OpAmps that might do it. If not, what external circuitry might you have to add?

 

Take a look at the topology and Bill of materials on this website:
http://www.instructables.com/id/Op-amp-based-PWM-genarator/

You want your harmonic distortion in this example to be the pulse width modulation out (PWM he has) to have that harmonic behavior your teacher describes. Take a look at the BOM study the op amp data sheet he describes and I did not help you.

 

I want to use two bjt 2N3904 as this is what I been taught in my class.

 

With only two BJT ?? Impossible, but you could try.

 

Well do you think four will do?

 

May do the job. Try Google "discrete op amps".
http://www.sg-acoustics.ch/analogue_audio/discrete_opamps/pdf/SGA-SOA-1_documentation.pdf