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How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.

- Thread starter Lightfuzz
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- #1

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How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.

- #2

Filip Larsen

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- #3

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- #4

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I've tried that but is there a way to actually solve it without guessing?

- #5

phyzguy

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- #6

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Do you only require a numerical solution given some particular boundry conditions?

- #7

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[tex] \frac{1}{2x}=\frac{\ddot{x}}{x}=-\frac{d}{dx}(\frac{1}{\dot{x}}) [/tex]

Then, reduce to a quadrature:

[tex]dt=(C-ln(\sqrt{x}))dx =d[x(C'-ln(\sqrt{x}))] [/tex]

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