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

How did they get this? PDE

  1. Nov 2, 2013 #1
    I've got this far on a pde (second last step) but have no idea how they got this equality(I'm a noob), could someone please explain? I was going to put this under homework but it is not homework and it doesn't really fit the template. Thanks in advance.

    Attached Files:

  2. jcsd
  3. Nov 2, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    It is an ordinary diff.eq,
    where dT/dt=-k*T, for a "k" with fluffy garments.
  4. Nov 3, 2013 #3


    User Avatar
    Science Advisor

    You can see that [itex]T(t)= Ae^{(ih/E)t}[/itex] does satisfy the equation by differentiating. As arildno says, you can just think of k= (ih/E) and use the fact that the derivtive of [itex]Ae^{kt}[/itex] is [itex]kAe^{kt}[/itex].

    If you are asking "how can we get that solution if we didn't notice that?", you need to integrate to go the other way:
    [tex]\dfrac{dT}{dt}= -\dfrac{ih}{E}T[/tex]
    separating variables,
    [tex]\dfrac{dT}{T}= -\dfrac{ih}{E}dt[/tex]
    [tex]\int\dfrac{dT}{T}= -\dfrac{ih}{E}dt[/tex]
    [tex]ln(T)= -\dfrac{ih}{E}t+ C[/tex]

    Now, take the exponential of both sides:
    [tex]T= e^{-\frac{ih}{E}t}e^C[/tex]
    and we let [itex]A= e^C[/itex].
  5. Nov 3, 2013 #4
    Thanksbut I got it a while ago now. sorry for not mentioning.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook