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find the differential equation of the family of the circles having thgeir centers at the origin

Sagot :

Family of Concentric Circles (circles having same center point, but different radii).

The equation that satisfies the family of concentric circles:

x² + y² = r²      

Differentiate x² + y² =r²

[tex]2x + 2y \frac{dy}{dx}= 0 [/tex]

[tex]x + y \frac{dy}{dx} =0[/tex]