I am quite ashamed of the level of my question, but I have this ODE -- it is a simplified version -- and my concern is only with the left hand side:$$ \dot v=kv$$which I need to rewrite in terms of c, and we have $c=\exp(-v^*/v) $, where $v^*$ is a constant. Hence $ v=-v^*/\ln c$, and personally, I would write:$$ \dot v = \frac{dv}{dc}\frac{dc}{dt}=\frac{v^*}{c\ln^2c}\dot c$$which leads to:$$\dot c=\frac{-kv^*}{\ln c} \frac{c\ln^2c}{v^*}=-kc\ln c$$However, a colleague of mine writes:$$ \dot v=\frac{v^*\dot c}{\ln^2c}$$which leads to:$$ \dot c=\frac{\ln^2c}{v^*}\frac{-kv^*}{\ln c}=-k\ln c$$Who's right? I am under the impression my version is the right one but my colleague says otherwise...Thanks for any help !
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