If a curve passes through (1,-2) and has slope x^2-2yx, it also passes through:

Question

If a curve passes through $(1,-2)$ and has slope $\dfrac{x^2-2y}{x}$, it also passes through:

Accepted Answer

$\dfrac{dy}{dx}+\dfrac2xy=x$. I.F.$=x^2$. $x^2y = \dfrac{x^4}{4}+C$; using $(1,-2)$: $C=-\dfrac94$.

$$y = \frac{x^2}{4}-\frac{9}{4x^2}.$$

This curve is satisfied by $(\sqrt3,0)$.

Solutions · 1