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Math Help - Solve the following ODE .. #3

  1. #1
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    Joined
    Sep 2010
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    98

    Solve the following ODE .. #3

    Problem:
    Solve the following equation:
    x^4y'=-x^3y-sec(xy)
    Solution:
    Rearrange:
    (x^3y+sec(xy))dx+x^4dy=0

    sec(xy)+x^3ydx+x^4dy=0

    sec(xy)+x^3(ydx+xdy)=0

    sec(xy)+x^3d(xy)=0

    Devide by sec(xy)x^3

    x^{-3}+cos(xy)d(xy)=0

    Now, I stopped.
    There is no dx with 1/x^3 so that i can integrate it!
    any help?
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  2. #2
    Member
    Joined
    Sep 2010
    Posts
    98
    I got it!
    I forgot to multpily the sec(xy) by dx in the first..
    so it will be:

    x^{-3} dx + cos(xy)d(xy)=0

    \implies \dfrac{-1}{2x^2}+sin(xy)=c
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