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    Find the general solution of the differential equation
     \displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x) .

    This one's a bit harder than the baby one earlier.
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    (Original post by Ano123)
    Find the general solution of the differential equation
     \displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x) .

    This ones a bit harder than the baby one earlier.
    What have you tried?
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    (Original post by Ano123)
    Find the general solution of the differential equation
     \displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x) .

    This one's a bit harder than the baby one earlier.
    I would not know where to start
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    (Original post by IYGB)
    I would not know where to start
    http://www.wolframalpha.com/input/?i...y%3Dtan(ln(x))
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    Don't just cheat and use wolframalpha. Try the question.
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    (Original post by Ano123)
    Don't just cheat and use wolframalpha. Try the question.
    I would...
    Spoiler:
    Show
    ...if I knew where to even begin.
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    (Original post by Zacken)
    What have you tried?
    Classic  x=e^t transforms it to  \displaystyle y'''(t)-2y''(t)-y'(t)+2y(t)=\tan (t) .
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    (Original post by Ano123)
    Classic  x=e^t transforms it to  \displaystyle y'''(t)-2y''(t)-y'(t)+2y(t)=\tan (t) .
    Can you take it from there?

    Hint: standard C.F and P.I works variation of parameters work
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    (Original post by Zacken)
    Can you take it from there?

    Hint: standard C.F and P.I works
    PI?
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    (Original post by Ano123)
    PI?
    Ah yeah, should have tried it myself. Go for variation of parameters instead.
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    (Original post by Zacken)
    Ah yeah, should have tried it myself. Go for variation of parameters instead.
    Bingo.
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    Wot bludy hel is this.
    Do i ned this for uni.



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    (Original post by physicsmaths)
    Wot bludy hel is this.
    Do i ned this for uni.



    Posted from TSR Mobile
    this is why you need to relearn DE's with me
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    (Original post by Ano123)
    Find the general solution of the differential equation
     \displaystyle x^3y'''+x^2y''-2xy'+2y=\tan (\ln x) .

    This one's a bit harder than the baby one earlier.
    Try differentiating it once or twice and see if you can substitute a fraction of the result(s) for tan(ln(x)) and set up through that sort of simultaneous equation an equation with fewer derivatives.
    (Note that the derivative of x^3 is 3x^2 (the one to the right go the term of x^3 in and the same is true for all the powers of x in there, and that the derivatives of y have the opposite pattern, meaning hopefully a technique like above will make some ground.)
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    (Original post by Ano123)
    Bingo.
    I was looking the variation of parameters method on the net but I cannot find anything with 3 derivatives.
    Are you making these up?
 
 
 
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