Show that $\frac{\mathrm{d}y}{\mathrm{d}x}$ when $x{{y}^{2}}-{{x}^{2}}y=1$ can be expressed as \

Question

Show that $\frac{\mathrm{d}y}{\mathrm{d}x}$ when $x{{y}^{2}}-{{x}^{2}}y=1$ can be expressed as $\frac{kxy-{{y}^{2}}}{kxy-{{x}^{2}}}$ where $k$ is a real number to be determined.

Accepted Answer

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-y^2}{2xy-x^2}$, so $k=2$ (shown).

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

Solution:

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