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

(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 A $(x + 1) \frac{d y}{d x} - y = 0$
Equation of straight line $y = m x + c$
If slope and y-intercept equal
then, $y = m x + m = m (x + 1)$
Differentiating it w.r.t x
$\frac{d y}{d x} = \frac{y}{(x + 1)}$
$(x + 1) \frac{d y}{d x} = y$
$(x + 1) \frac{d y}{d x} - y = 0$

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