Question

If x=tan(1/a .logy),show that (1+x^2) dy/dx=ay

Answer 1

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$x = tan( \frac{1}{a} \: logy \: )$

$\implies \: {tan}^{ - 1} x \: = \frac{ log(y) }{a}$

Differentiating both sides with respect to x

$\frac{1}{1 + {x}^{2} } = \frac{1}{a} \times \frac{1}{y} \frac{dy}{dx}$

$\therefore \: \: (1 + {x}^{2} ) \frac{dy}{dx} = ay$

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