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Math Help - whats wrong with my solution

  1. #1
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    whats wrong with my solution

    the last integral does not integrate :

    xy' - y=ln(y);  x=(ln(y) + y)/y'; y' = p;  x=(ln(y) + y)/p;

    dx=-1/p^2 (ln(y) + y)dp + (1/yp + 1/p)dy;

    (ln(y)/p^2 + y/p^2)dp=dy/yp;  dp/p = dy/(yln(y)+y^2)
    Last edited by mr fantastic; April 1st 2010 at 03:40 AM. Reason: Added spacing for better readability
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  2. #2
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    Quote Originally Posted by noteiler View Post
    the last integral does not integrate :

    xy' - y=ln(y); x=(ln(y) + y)/y'; y' = p; x=(ln(y) + y)/p;

    dx=-1/p^2 (ln(y) + y)dp + (1/yp + 1/p)dy;

    (ln(y)/p^2 + y/p^2)dp=dy/yp; dp/p = dy/(yln(y)+y^2)
    The solution involves an integral that cannot be found using a finite number of elementary functions: integrate 1/(Log[y] + y) - Wolfram|Alpha

    Where has the DE come from?
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  3. #3
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    this DE was given to me by university tutor. and yes, i know that function doesn't integrate in elementary functions, but i thought that i am doing something wrong. by the way i have plenty DEs that i can't solve duo to integration for example in attachment. i think that i'm just doing something wrong. can someone help me.
    Attached Thumbnails Attached Thumbnails whats wrong with my solution-img_1254.jpg  
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