#(dR)/(dS) = k (R/S)# R=?

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Answer 1 · 2018-06-28T17:27:11

#R = CS^k# where C is an arbitrary constant.

Given: #(dR)/(dS) = k (R/S)#

Use the separation of variables method:

#(dR)/R = k (dS)/S#

Integrate both sides:

#int(dR)/R = kint (dS)/S#

#ln(R) = kln(S)+ C#

#ln(R) = ln(S^k)+ C#

#e^(ln(R)) = e^(ln(S^k)+ C)#

#R = e^Ce^ln(S^k)#

#R = e^CS^k#

#R = CS^k# where C is an arbitrary constant.