The differential equation of family of straight lines whose slope is equal to $y -$ intercept is

(x + 1) \frac{d y}{d x} + y = 0

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

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\frac{d y}{d x} = \frac{x + 1}{y + 1}

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\frac{d y}{d x} = \frac{x - 1}{y - 1}

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Solution

The correct option is B $(x + 1) \frac{d y}{d x} - y = 0$
$y = m x + c$
When Slope- y intercept
$y = m x + m$ $y = m (x + 1)$
$\frac{d y}{d x} = m$
$\frac{d y}{d x} = \frac{y}{x + 1}$
$\frac{d y}{d x} (x + 1) - y = 0$
$B$ is correct.

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