$(dR)/(dS) = k (R/S)$ 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.

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