Kumbhakar–Roy–Srinivasan classification conjecture for first-order differential equations

Let $(k,\delta)$ be a differential field of characteristic zero with field of constants $C$. Consider a first-order differential equation over $k$, and, respectively, an autonomous differential equation over $C$. A differential field extension of $k$ is required to have $C$ as its field of constants. Kumbhakar–Roy–Srinivasan classification conjecture. A first-order differential equation over $k$ (respectively, an autonomous differential equation over $C$) is not of general type if and only if it has at most three (respectively, at most one) algebraically independent solutions in any given differential field extension of $k$ having $C$ as its field of constants. The conjecture concerns an existential classification of differential equations under the restriction to extensions introducing no new constants. The source paper states that this conjecture is proved there, so its resolution is established in the paper.