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  1. #1
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    Help =)

    Having problems solving this diff equation.

    (1-x^2)y+ xy = x for -1 < x < 1

    I get the nt factor to 1/(1-x^2)^0,5, But having problems after that.


    Thank you.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by echo123 View Post
    Having problems solving this diff equation.

    (1-x^2)y+ xy = x for -1 < x < 1

    I get the nt factor to 1/(1-x^2)^0,5, But having problems after that.


    Thank you.
    does post #21 here help?
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  3. #3
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    Hello again

    Not really,,I understand the general approach to solving a diff equation its just that I cant get the right side to be a single derivate. having problems there.
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  4. #4
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    Im sorry, I meant the left side =)
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by echo123 View Post
    Hello again

    Not really,,I understand the general approach to solving a diff equation its just that I cant get the right side to be a single derivate. having problems there.
    ok, so following the steps exactly, you would end up with

    \frac 1{\sqrt{1 - x^2}}y' + \frac x{(1 - x^2)^{3/2}}y = \frac x{(1 - x^2)^{3/2}}

    again, just following the steps i outlined (we literally don't have to think about this if we know the steps by heart), this becomes

    \left( \frac 1{\sqrt{1 - x^2}}y\right)' = \frac x{(1 - x^2)^{3/2}}

    now integrate both sides and continue


    look closely at the steps and see what is confusing you. the single derivative is simply the coefficient of y' times y.
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  6. #6
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    Oh,, I did exatly that but I thought it was wrong. Thank you very much.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by echo123 View Post
    Oh,, I did exatly that but I thought it was wrong. Thank you very much.
    you're welcome

    next time have more confidence in yourself and tell us what you did, so we can give you a pat on the back
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  8. #8
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    I messed up when I multiplied the coefficient of y' and y. I Do that to check that im on the right track but this time it turned out bad =(.
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