Question

Find differential equation of the equation - x^2+y^2 = 2ax

Answer 1

Step-by-step explanation:

We have,

${x}^{2} + {y}^{2} = 2ax$

$\implies2{x} + 2{y} \cdot \dfrac{dy}{dx} = 2a$

$\implies{x} + {y} \cdot \dfrac{dy}{dx} = a$

Put this value in original equation,

${x}^{2} + {y}^{2} = 2x \cdot \left(x + y \dfrac{dy}{dx} \right)$

$\implies \: {x}^{2} + {y}^{2} = 2x ^{2} +2x y \dfrac{dy}{dx}$

$\implies \: {y}^{2} = {x}^{2} +2x y \dfrac{dy}{dx}$

$\implies \: 2x y \dfrac{dy}{dx} ={y}^{2} - {x}^{2}$

$\implies \: \dfrac{dy}{dx} = \dfrac{{y}^{2} - {x}^{2} }{2xy}$