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Differential Equations IVP

  1. Sep 18, 2008 #1
    Use the variable change u = ln(y) to solve the IVP dy/dt = -y ln(y), y(1) = 2?

    We haven't covered this in class yet so I do not know where to even start.
     
  2. jcsd
  3. Sep 18, 2008 #2

    gabbagabbahey

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    Well, you're given [tex] u(t)=ln(y(t)) [/tex], so why not calculate [tex]y(t)[/tex] in terms of [tex] u(t) [/tex] and then differentiate to get [tex] \frac{dy}{dt} [/tex] in terms of [tex] u(t) [/tex] and [tex] \frac{du}{dt} [/tex] and then substitute these into your differential equation to get a DE in terms of u instead of y. What do you get when you do this?
     
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