The differential equation of the family of st | vedclass

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(A) The equation of a straight line with slope $m$ and $y$-intercept $c$ is given by $y = mx + c$. Given that the slope is equal to the $y$-intercept,

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$(x+1) \frac{dy}{dx} - y = 0$

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(A) The equation of a straight line with slope $m$ and $y$-intercept $c$ is given by $y = mx + c$. Given that the slope is equal to the $y$-intercept,we have $m = c$. Substituting this into the line equation,we get $y = cx + c = c(x+1)$. Differentiating both sides with respect to $x$,we get $\frac{dy}{dx} = c$. Substituting the value of $c$ from the first equation into the derivative,we have $\frac{dy}{dx} = \frac{y}{x+1}$. Rearranging the terms,we get $(x+1) \frac{dy}{dx} - y = 0$.

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

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