Question

The differential equation $y\frac{dy}{dx}+x=A$ where A is a constant represents a set of:

• A. circles centred on y axis
• B. circles centred on x axis
• C. parabolas
• D. ellipses

Answer 1

The correct option is B circles centred on x axis

$y\frac{dy}{dx}=A-x$

$\Rightarrow ydy=(A-x)dx$

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

$\frac{y^2}{2}=\frac{2Ax-x^2+c}{2}$

$y^2=-(x^2-2Ax+A^2)+A^2+c$

$\Rightarrow (x-A{)}^2+y^2=A^2+c$

$\Rightarrow$ center of circle = (A,0)