A curve through $(2,1)$ satisfies $(x^2+y^2)\dfrac{\mathrm{d}y}{\mathrm{d}x}=2xy$ for $x0$ an

Question

A curve through $(2,1)$ satisfies $(x^2+y^2)\dfrac{\mathrm{d}y}{\mathrm{d}x}=2xy$ for $x>0$ and $y>0$. Find an implicit equation for the curve and hence find the exact value of $y$ when $x=3$.

Accepted Answer

$x^2-y^2=3y;\quad y(3)=\dfrac{3}{2}(\sqrt5-1)$

Quadratic relation through (2, 1)

Quadratic relation through (2, 1)

Solution:

Solution locked