Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How does dy/dt=ry end up with the constant multiple on the right?

  1. Sep 11, 2013 #1
    I have, from the textbook:

    dy/dt = ry

    So I solve and get y = e^(rt)+C

    However, the book says that y=y_0 * e^(rt), where y_0 is the answer to the initial condition, y(0).

    I don't get it. The + C should be what we use to solve for the initial condition; how does y_0 end up in the same term with the exponential?

  2. jcsd
  3. Sep 11, 2013 #2
    integrating dy/y=rdt leads to ln(y)=rt+C

    this leads to y=exp(rt+C)
    but exp(rt+C)=exp(C)*exp(rt)
    and you simply replace the constant exp(C) by a new constant C

    EDIT: your mistake was most likely that you didn't include the constant of integration immediately after integrating, but after getting rid of the logarithm.
  4. Sep 11, 2013 #3
    Yes! I see. Thank you.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook