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.