Question

The $D.E$ $y\frac{dy}{dx}+x=a$ represents

• A. a circle whose centra is on $X-$axis
• B. a circle whose centre is on $Y-$axis
• C. a circle whose centre is origin
• D. a parabola

Answer 1

The correct option is A a circle whose centra is on $X-$axis

$y\frac{dy}{dx}+x=a$

$\Rightarrow ydy+xdx=adx$

Integrating both sides

$\Rightarrow \frac{y^2}{2}+\frac{x^2}{2}=ax+c$

$\Rightarrow x^2+y^2=2ax+c$

$\Rightarrow x^2+y^2-2ax+c=0$

on comparing it with

$x^2+y^2+2gx++2fy+c=0$

here , $g=-a,f=0$

centre =$\left(-g,-f\right)=\left(a,0\right)$

therefore , it represent a circle with centre at X- axis