Question

what is the general solution of
$\frac{dy}{dx} = - \frac{x}{y}$
​

Answer 1

Given Question :-

What is the general solution of

$\sf \: \dfrac{dy}{dx} = - \dfrac{x}{y}$

ANSWER

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

$\rm :\implies\:y \: dy \: = \: - \: x \: dx$

• On integrating both sides, we get

$\rm :\implies\: \int \: y \: dy \: = - \int\ x \: dx$

$\rm :\implies\:\dfrac{ {y}^{2} }{2} = - \dfrac{ {x}^{2} }{2} + \dfrac{c}{2}$

$\rm :\implies\: {y}^{2} = - {x}^{2} + c$

$\rm :\implies\: {y}^{2} + {x}^{2} = c$