The differential equation for the family of ellipses (foci on either axis, centre at origi…

Question

The differential equation for the family of ellipses (foci on either axis, centre at origin) through $(0,3)$ is:

Accepted Answer

$\dfrac{x^2}{a^2}+\dfrac{y^2}{9}=1$; through $(0,3)$ gives $b^2=9$. Differentiating twice and eliminating $a^2$ leads to $xyy''+x(y')^2-yy'=0$.

Solutions · 1