Q119 / 180 · COMEDK 2020 · Mathematics

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

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

We have, equation of line is $$ y=m x+C $$ But $m=C$ (given) $$ \therefore \quad y=C x+C $$ $\operatorname{Now}, \frac{d y}{d x}=C$ $$ \therefore \quad y=\frac{d y}{d x}(x+1) \Rightarrow(x+1) \frac{d y}{d x}-y=0 $$ which is required differential equation.

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

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