If the differential equation representing the family of circles touching the x-axis at the…

Question

If the differential equation representing the family of circles touching the $x$-axis at the origin is $(x^2-y^2)\dfrac{dy}{dx}=g(x)y$, then $g(x)$ equals:

Accepted Answer

Family: $x^2+y^2-2ay=0$. Differentiating and eliminating $a$ gives $(x^2-y^2)\dfrac{dy}{dx}=2xy$, so $g(x)=2x$.

Solutions · 1