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Math Help - I need to solve this D. E. (( plz help ) #2

  1. #1
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    I need to solve this D. E. (( plz help ) #2

    and this one also
    Attached Thumbnails Attached Thumbnails I need to solve this D. E. (( plz help ) #2-untitled-2.jpg  
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  2. #2
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    Suppose you had x-e^x=c and you know that if you can put it into the form k=ge^{g}, then you can take the Lambert W function of both sides and obtain g=W(k). So, can you get x-e^x=c into the form -(x-c)e^{-(x-c)}=-e^{c} and then taking the W function of both sides get  -(x-c)=W(-e^{c}). Alright then, now do it with y', isolate y', and then integrate.

    . . . oh yeah . . . end special function discrimination: Equal rights for special functions!

    . . . same dif with the other one too. Pretty sure anyway, haven't worked it out and checked it though.
    Last edited by shawsend; June 28th 2009 at 06:24 AM.
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  3. #3
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    Quote Originally Posted by shawsend View Post
    Suppose you had x-e^x=c and you know that if you can put it into the form k=ge^{g}, then you can take the Lambert W function of both sides and obtain g=W(k). So, can you get x-e^x=c into the form -(x-c)e^{-(x-c)}=-e^{c} and then taking the W function of both sides get  -(x-c)=W(-e^{c}). Alright then, now do it with y', isolate y', and then integrate.

    . . . oh yeah . . . end special function discrimination: Equal rights for special functions!

    . . . same dif with the other one too. Pretty sure anyway, haven't worked it out and checked it though.
    thnx alout my frind
    i'll try it and came back to you
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