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Math Help - Differential Equations

  1. #1
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    Differential Equations

    Please help me solve:

    1. y'(1+y'^{2})=ay''

    2. y^{3}y''=1

    3. xy''=y'ln\frac{y'}{x}
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    1 and 3 are reduced to first order by putting t=y'.
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  3. #3
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    Quote Originally Posted by sinichko View Post
    Please help me solve:
    [snip]

    2. y^{3}y''=1

    [snip]
    \frac{d^2y}{dx^2} = \frac{1}{y^3} is solved by first making the substitution \frac{d^2 y}{dx^2} = \frac{d}{dy}\left[ \frac{v^2}{2}\right] where v = \frac{dy}{dx} and solving for v.
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