If y=xx,prove that dx2d2y−y1(dxdy)2−xy=0

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If {y}={x}^{{x}},prove that {{{d}^{{2}}{y}}}{{{.{d}{x}.}^{{2}}

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If $y = x^{x},$ prove that $\frac{d ^{2} y}{d x ^{2}} - \frac{1}{y} (\frac{d y}{d x})^{2} - \frac{y}{x} = 0$

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Alexander Discussed

y = x^{x},

prove that

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{y} (\frac{d y}{d x})^{2} - \frac{y}{x} = 0

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Question Text

y = x^{x},

prove that

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{y} (\frac{d y}{d x})^{2} - \frac{y}{x} = 0