Question

The differential equation $y\frac{dy}{dx}+x=c$ represents:

• A. a family of hyperbolas
• B. a family of circles whose centres are on the y-axis
• C. a family of parabolas
• D. a family of ellipse
• E. a family of circles whose centres are on the x-axis

Answer 1

Answer: (E)

We have, $y\frac{dy}{dx}+x=c$ On it can be rewritten as $ydy=(c-x)dx$ On integrating both sides, we get $\int ydy=\int (c-x)dx$ $\frac{y^2}{2}=cx-\frac{x^2}{2}+c_1$ $\Rightarrow x^2+y^2-2cx=c_1$ Which represents a family of circles whose centre is (c, 0) i. e., on the $x-$ axis.