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Thread: Differential Equations

  1. #1
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    Differential Equations

    Please help me solve:

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

    2. $\displaystyle y^{3}y''=1$

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

    2. $\displaystyle y^{3}y''=1$

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