Calculus of a Single Variable, Chapter 6, 6.3, Section 6.3, Problem 6

(dr)/(ds)=0.75s
This differential equation is separable since it has a form

N(y) (dy)/dx=M(x)
And, it can be re-written as
N(y) dy = M(x) dx
So separating the variables, the equation becomes
dr = 0.75s ds
Integrating both sides, it result to
int dr = int 0.75s ds
r + C_1 = 0.75s^2/2 + C_2
r+C_1 = 0.375s^2+C_2
Isolating the r, it becomes
r = 0.375s^2+C_2-C_1
Since C2 and C1 are constants, it can be expressed as a single constant C.
r = 0.375s^2 + C

Therefore, the general solution of the given differential equation is r = 0.375s^2 + C .