CUET Preparation Today
The differential equation $\frac{dy}{dx}+\frac{x}{y}=0$, represents the family of curves: |
$x^2-y^2=C$ $\frac{x}{y}=C$ $xy=C$ $x^2+y^2=C$ |
$x^2+y^2=C$ |
$\frac{dy}{dx}+\frac{x}{y}=0⇒\frac{dy}{dx}=\frac{-x}{y}$ $y\,dy=-x\,dx$ Integrating both sides $\int y\,dy=\int-x\,dx$ $⇒\frac{y^2}{2}=\frac{-x^2}{2}+C$ $⇒x^2+y^2=2C$ $⇒x^2+y^2=C$ |
