Question

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

• A. $(x+1) \frac {dy} {dx}+y=0$
• B. $(x+1) \frac {dy} {dx}-y=0$
• C. $ \frac {dy} {dx}= \frac {x+1}{y+1}$
• D. $ \frac {dy} {dx}= \frac {x-1}{y-1}$

Answer 1

Answer: (B)

Equation of line whose slope is equal to y intercept, is
$y = cx + c = c(x + 1) \,\,\,\,\dots(i)$
$\Rightarrow \, \frac{dy}{dx} = c\,\,\,\,\dots(ii)$
On putting the value of c from Eq. (i) in Eq. (ii),
we get $\frac{dy}{dx} = \frac{y}{x +1}$
$\Rightarrow \, (x + 1) \frac{dy}{dx} - y = 0 $
Which is the required differential equation.