Question

The differential equation corresponding to the family of curves $y=cx+c-c^2$ where `c` is a parameter.

• A. $y_1^2+(x+1)y_1-y=0$
• B. $y_1^2-(x+1)y_1+y=0$
• C. $y_2-x{y}_1+y=0$
• D. $y_1{y}_2-xy=0$

Answer 1

The correct option is B $y_1^2-(x+1)y_1+y=0$

$y=cx+c–c^2\Rightarrow \frac{dy}{dx}=c$
$\therefore y=x.\frac{dy}{dx}+\frac{dy}{dx}+-{\left(\frac{dy}{dx}\right)}^2$
$\Rightarrow y=(x+1)y_1-y_1^2$