Question about bistable multivibrator op amps

[theBEAST]

Homework Statement

Here is the problem:

So this is a bistable multivibrator.

Homework Equations

KVL and KCL laws

The Attempt at a Solution

I don't entirely understand bistable multivibrators. I get what the solution is, the input voltage caps at 0.1V and the output caps at 0.7V and hysteresis occurs. Apparently, the output voltage will feed back into the + terminal of the op amp and this loops repeats itself until saturation... Why doesn't this happen with a regular non-inverting amplifier. The configuration is almost the same except the terminals are flipped... What does this mean?

However, when I do some circuit analysis I notice that if the input is greater than 0.1V weird things happen. For example take a look at what I did here:

So when you have 5V as the input, what happens to the current flow, does some of it just magically get capped?

Another question I have is what is that 10k resistor right after the op amp used for?

 

[NascentOxygen]

The equality v(+) = v(-) for an op-amp holds only while the op-amp is operating linearly and ouput is not saturated.

If those conditions are not met, then it's the case that
v(+) _≠ v(-)

 

[rude man]

Your feedback here is positive. In a linear noninverting amplifier the feedback is negative. BIG difference!

Use the fact that the op amp output is +12V if input V+ is higher than input V- , and -12V if V- > V+.

So you're always comparing input voltages V+ vs. V- as you vary the V- voltage back & forth. Hint: limit your V- input swing to +/- 0.2V.

The 10K output resistor limits the op amp output current to a safe value.