Differential Equations · Variable separable differential equations

Flawed question. Ill-posed: the solution with $y(0) = 1/2$ blows up near $x = 0.99$ (its arctangent would have to reach $11\sqrt3/12 > \pi/2$), so $y(1)$ does not exist; the keyed (3) is only a formal value (about $-102$, impossible for an increasing $y$ starting at $1/2$), and no minimal change gives a valid question with these options. It is shown for completeness and is left out of practice tests.