The differential equationy `y (dy)/(dx)+x=a` (a is any constant) represents

Options

A. A set of straight lines
B. A set of elipes
C. A set of circles
D. None of the above

Answer

A

Explanation

Given diff. equation is
` y(dy)/(dx) +x=a`
` Rightarrow y(dy)/(dx) =a -x`
` Rightarrow ydy = (a-x) dx`
`int y dy = int (a -x) dx `
` Rightarrow y^(2)/2 =ax -x^(2)/2 +k`
` Rightarrow x^(2) +y^(2) -2 ax =2k`
which represents a set of circles.