When the electromotive force (emf) is removed from a circuit containing inductance and resistance but no capacitors, the rate of decrease of current is proportional to the current. If the initial current is 30 amps but decays to 11 amps after 0.01 seconds, find an expression for the current as a function of time.
Do I use the $y^{\prime}=-ky$ ? or $y^{\prime}=\dfrac{-k}{y}$
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$\begingroup$THanks to @in_wolfram_we_trust.
This is my solution, hope its correct.
Using $\dfrac{dy}{dt} = -ky$ with the given conditions $y=30, t = 0$ and $y = 11, t = 0.01$
$\dfrac{\mathrm{d}y}{\mathrm{d}t} = -ky$ collect the varibles together.
$\int \frac{\mathrm{d}y}{y} = \int -k\; \mathrm{d}t$
results to $y = Ce^{-kt}$
$30 = Ce^{-k\left(0\right)} \Rightarrow C = 30$
$11 = 30e^{-k\left(0.01\right)} \Rightarrow -k = \dfrac{\ln{\vert 11/30 \vert}}{0.01} \Rightarrow k = 100.3$
Thus the equation is $y=30e^{-100.33t}$
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