The equation of the curve in which sub-normal varies as the square of the ordinate is ( $k$ is constant of proportionality)

y = A e^{2 k x}

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y = e^{k x}

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y^{2} / 2 + k x = A

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y^{2} + k x^{2} = A

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Solution

The correct option is B $y = e^{k x}$
$| y \frac{d y}{d x} | = k y^{2}$
$\frac{d y}{d x} = k y$
$\frac{d y}{y} = k . d x$
Integrating both sides
$l n y = k x + c$
$y = e^{k x} . e^{c}$
Or
$y = C e^{k x}$ where $C = e^{c}$ .

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