Solving a Differential Equation for Distortion

Can someone give me a bit more explanation as to how I should be solving a differential equation to replicate an analog distortion pedal? I’ve been reading a lot but I’m a bit confused. Based on the thesis paper by David Yeh I’ve found a DE to model a diode clipper circuit:
diode clipper

Now I understand I can do some topology preserving transform to this equation first but I may simply use a numerical method like Newton Raphson to solve the equation. Does anyone have any example of this in code? If I fill in for known values, I get

dVo / dt = (Vi(t) - Vo) / (2200 * 0.00000001) - 2(0.0000000252/0.00000001)sinh(Vo/0.0453)

I also don’t understand what the function Vi(t) should be though I understand it should be some function that satisfies this equation.

Have a look at that book, everything is explained in detail there:

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Thank you. I’ll go about actually reading that one. I’ve looked at it before but it’s pretty tough. I’ll just have to spend more time with it.

Is there a good space for me to ask questions as I work through that text?

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Awesome thanks!