what does the differential equation ` y(dy)/(dx) +x =a `
(where a is a constant) represent ?

Options

A. A set of circles having centre on the Y-axis
B. A set of circles having centre on the X -axis
C. A set ellipes
D. A pair of straight lines

Answer

B

Explanation

Given differential equation is
` (ydy)/(dx) +x =a`
` Rightarrow ydy +xdx =adx`
Integrate on both sides, we get
`int y dy + int xdx = int adx`
` Rightarrow (y^(2))/2 + x^(2)/2 =ax +c`
where c is a constant of integration.
` Rightarrow y^(2) =x^(2) -2ax =c`
Thois represents a cicle whose centre is on the X-axis.