Question

what is ds/dr=ks

Answer 1

That means you're differentiating s with respect to r, and that ks is a differential of an equation with lhs as r.

Answer 2

\[\frac{ ds }{ dr } =ks \rightarrow \frac{ ds }{ s} =k \times dr \\ \int\limits \frac{ ds }{ s } =\int\limits k dr \\ln|s|=kr +constant \\s=c \times e^{kr}\]