Q114 / 180 · KCET 2007 · Mathematics

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

  • Correct answer
    A
    $(x+1) \frac{d y}{d x}-y=0$
  • B
    $(x+1) \frac{d y}{d x}+y=0$
  • C
    $\frac{d y}{d x}=\frac{x-1}{y-1}$
  • D
    $\frac{d y}{d x}=\frac{x+1}{y+1}$

Solution

Equation of line whose slope is equal to $y$ intercept, is $$ \Rightarrow \quad \begin{aligned} y &=c x+c=c(x+1) \\ \frac{d y}{d x} &=c \end{aligned} $$ On putting the value of $c$ from Eq. (i) in Eq. (ii), we get $\frac{d y}{d x}=\frac{y}{x+1}$ $$ \Rightarrow \quad(x+1) \frac{d y}{d x}-y=0 $$ which is the required differential equation

Hence, the correct answer is option: 'A'.

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