If you can solve this Differential Equation, then do it correctly!?

Question

In trying to model the response to a stimulus, psychologist use the Weber Fechner Law. This law states that the rate of a response r, with respect to a stimulus s, is inversely proportional to the stimulus. Write a differential equation to model this law. Solve the differential equation if r(s0)= r0 for some initial stimulus s0,

Answer 1

dr/ds = a/s where a is the constant of proportionality.
dr = (a/s) ds
integrate both sides
r = a ln |s| + c
r(s0) = a ln |s0| + c = r0
c = r0 - a ln|s0|

r(s) = a ln |s| - a ln|s0| + r0
r(s) = a ( ln|s| - ln|s0| ) + r0
r(s) = a ln |s /s0| + r0
If s is never a negative quantity you can replace the absolute value with parentheses.