Determining U_ref on Schmitt Trigger
What have we got?


Op-amp is ideal. It's a Schmitt trigger so output will be +15 V or -15 V.


Let's start with condition that output is low (-15 V) and Uin is on the point of switching the output high.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Output is about to switch high.

$$ V_+ = U_{out} + \frac {(U_{in} - U_{out}) R_2}{R_1+R_2} = -15 + \frac {(3 - (-15)) R_2}{1k+R_2} = -15 + \frac {18\cdot R_2}{1k+R_2} \tag 1$$







simulate this circuit

Figure 2. Output is high but input is at the lower threshold.

$$ V_+ = U_{out} + \frac {(U_{in} - U_{out}) R_2}{R_1+R_2} = 15 + \frac {(2 - 15) R_2}{1k+R_2} = 15 - \frac {13 \cdot R_2}{1k+R2} \tag 2$$

Solving simultaneously:

$$-15 + \frac {18\cdot R_2}{1k+R_2} = 15 - \frac {13 \cdot R2}{1k+R2} \tag 3$$

$$ \frac {31 \cdot R_2}{1k+R_2} = 30 \tag 4 $$

$$ \frac {R_2}{1k+R_2} = \frac {30}{31} \tag 5 $$

$$ {R_2} = \frac {30}{31}k + \frac {30}{31}R_2 \tag 6 $$
$$ \frac {1}{31}R_2 = \frac {30}{31}k \tag 7 $$

You should be able to solve for R2 and thensolve for Uref.

I haven't double-checked this or finished the calculations. Let me know if this works.