COMEDK · Maths · 32. Differential Equations
Solution of the differential equation \(y \dfrac{d y}{d x}+x=0\) represents a family of
- A Ellipse
- B Circles
- C Parabola
- D Hyperbola
Answer & Solution
Correct Answer
(B) Circles
Step-by-step Solution
Detailed explanation
The given differential equation is \(y \dfrac{dy}{dx} + x = 0\). Rearranging the terms, we have \(y \dfrac{dy}{dx} = -x\). Integrating both sides with respect to \(x\), we get \(\int y \, dy = - \int x \, dx\). This yields \(\dfrac{y^2}{2} = -\dfrac{x^2}{2} + C\), where \(C\) is…
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