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Simplifying an ODE into explicit form

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data
    So i think i found the general solutions to both these separable equations, but im not sure if im suppose to simplify any further to get it in explicit form, and how i can even do that.

    2. Relevant equations



    3. The attempt at a solution

    1. [itex]\frac{dy}{dx}[/itex] - [itex]\frac{x+e^{-x}}{y+e^{y}}[/itex] = 0

    2. [itex]\frac{dx}{dt}[/itex] = te[itex]^{x+t}[/itex]

    For 1), i get [itex]\frac{y^{2}}{2}[/itex]+e[itex]^{y}[/itex] = [itex]\frac{x^{2}}{2}[/itex]-e[itex]^{-x}[/itex]+C

    and for 2) i get:

    -e[itex]^{-x}[/itex]+C = te[itex]^{t}[/itex]-e[itex]^{t}[/itex]

    Are these right? and is there anyway to simplify them into explicit form? Thanks
     
  2. jcsd
  3. Jan 13, 2012 #2

    LCKurtz

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    They are both correct. You can't solve the first one for y explicitly with the usual functions. You could solve the second for x if you wanted to using logarithms.
     
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