Given that $y$ is a function with respect to $x$ and that $xy^{2} - x^{2}y = m$, pro

Question

Given that $y$ is a function with respect to $x$ and that $xy^{2} - x^{2}y = m$, prove that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{kxy - y^{2}}{kxy - x^{2}}$, where $m$ is fixed and $k$ is a constant to be determined. Work where $2xy-x^2\ne0$.

Accepted Answer

$k=2$, with $m$ an arbitrary fixed constant; $y'=(2xy-y^2)/(2xy-x^2)$ where the denominator is nonzero.

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

Video Solution:

Solution:

Solution locked