The differential equation of the family of straight lines whose slope is equal to y-intercept is
A. $\frac{d y}{d x}=\frac{x-y}{y-1}$
B. $\frac{d y}{d x}=\frac{x+1}{y+1}$
C. $(x+1) \frac{d y}{d x}-y=0$
D. $(x+1) \frac{d y}{d x}+y=0$
E. $\frac{d y}{d x}-\frac{x+1}{y+1}=0$
Choose the correct answer from the given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - C only
let eq. be $\frac{x}{a}+\frac{y}{b}=1$ ...(1)
$\frac{dy}{dx}=b$
differentiating (1) w.r.t. x
$\frac{1}{a}+\frac{1}{b}\frac{dy}{dx}=0$
$\frac{1}{a}++1=0⇒a=-1$
from (1) $-x+\frac{y}{b}=1$
so $y=b(x+1)$
$y=\frac{dy}{dx}(x+1)$
$\frac{dy}{dx}(x+1)-y=0$