Number of straight lines which satisfy the differential equation $\frac{d y}{d x} + x {(\frac{d y}{d x})}^{2} - y = 0$ is:

1

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2

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3

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4

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Solution

The correct option is A $2$
$y = m x + c$ $\Rightarrow \frac{d y}{d x} = m$
It satisfies $\frac{d y}{d x} + x {(\frac{d y}{d x})}^{2} - y = 0$
$m + x m^{2} - m x - c = 0$
$x (m^{2} - m) + (m - c) = 0$
This is an identify so
$m = 0$ or $m = 1$ & $c = m$
So two such line are possible

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