The differential equation $\frac{dy}{dx}

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

The differential equation $\frac{dy}{dx}+\frac{x}{y}=0$, represents the family of curves:

Options:

$x^2-y^2=C$

$\frac{x}{y}=C$

$xy=C$

$x^2+y^2=C$

Correct Answer:

$x^2+y^2=C$

Explanation:

$\frac{dy}{dx}+\frac{x}{y}=0⇒\frac{dy}{dx}=\frac{-x}{y}$

$y\,dy=-x\,dx$

Integrating both sides

$\int y\,dy=\int-x\,dx$

$⇒\frac{y^2}{2}=\frac{-x^2}{2}+C$

$⇒x^2+y^2=2C$

$⇒x^2+y^2=C$