Number of straight lines which satisfy the different 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 B $2$
Let $y = m x + c$ of a solution of given D.E.

Then $\frac{d y}{d x} = m$

So $m + x m^{2} - (m x + c) = 0$

$\Rightarrow m + (m^{2} + m) n + c = 0$

$\Rightarrow m^{2} - m = 0; m + c = 0$

$\Rightarrow m (m - 1) = 0$

$m = 0$ or $1$

Of $m = 0, c = 0; m = 1, c = + 1$

Lines are $y = 0 a n d y = x + c$

$y = x + 1$

Two lines are possible

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