This is surely the simplest problem imaginable in DE, but it's been a few years and I'm having trouble recalling. The goal of my task doesn't necessitate relearning DE, so I thought I would take a shot at asking directly.(adsbygoogle = window.adsbygoogle || []).push({});

Simply, I wish to express the time-dependent rate equation [itex]\frac{dy(t)}{dt}=x-\frac{y(t)}{z}[/itex] as a function of time where [itex]x[/itex] and [itex]z[/itex] are known constants. I've been given a solution of [itex]y(t)=xz(1-e^{-t/z})[/itex] but I would very much like to remember how to get there. I do not have initial conditions, although [itex]y(0)=0[/itex] is a fair assumption for this problem.

Thank you very much in advance.

Note: this is not homework for a DE course.

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# Expressing time-dependent ODE

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