Question

помогите пожалуйста ​

Answer 1

$(1 - {x}^{2} )dy = xydx$

$(1 - {x}^{2} )y' = xy$

$y' = \frac{xy}{1 - {x}^{2} }$

$1 - {x}^{2} = 0$

$x_1 = 1$ $x_2 = -1$

$\frac{dy}{y} = \frac{xdx}{1 - {x}^{2} }$

$\int\frac{dy}{y} = \int \frac{xdx}{1 - {x}^{2} }$

$ln |y | = - \frac{ln | {x}^{2} - 1| }{2} + ln |C|$

$2ln |y| = ln |C| - ln | {x}^{2} - 1 |$

${y}^{2} = \frac{C}{{x}^{2}-1}$

$x_1 = 1$ $x_2 = -1$