Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 $y^{\prime}=\dfrac{-k}{y}$

share|cite|improve this question
If $a$ is proportional to $b$ then $a = kb$. (With constant $k$ possibly negative). – in_wolframAlpha_we_trust Feb 22 '13 at 7:25
@in_wolfram_we_trust what do you think of my answer – yiyi Feb 22 '13 at 8:38
up vote 1 down vote accepted

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 $y=30e^{-100.33t}$

share|cite|improve this answer
That looks good. – in_wolframAlpha_we_trust Feb 22 '13 at 8:56

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.