[tex](1 - {x}^{2} )dy = xydx[/tex]
[tex](1 - {x}^{2} )y' = xy [/tex]
[tex]y' = \frac{xy}{1 - {x}^{2} } [/tex]
[tex] 1 - {x}^{2} = 0 [/tex]
[tex] x_1 = 1 [/tex] [tex] x_2 = -1 [/tex]
[tex] \frac{dy}{y} = \frac{xdx}{1 - {x}^{2} } [/tex]
[tex] \int\frac{dy}{y} = \int \frac{xdx}{1 - {x}^{2} } [/tex]
[tex]ln |y | = - \frac{ln | {x}^{2} - 1| }{2} + ln |C| [/tex]
[tex]2ln |y| = ln |C| - ln | {x}^{2} - 1 | [/tex]
[tex] {y}^{2} = \frac{C}{{x}^{2}-1} [/tex]
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[tex](1 - {x}^{2} )dy = xydx[/tex]
[tex](1 - {x}^{2} )y' = xy [/tex]
[tex]y' = \frac{xy}{1 - {x}^{2} } [/tex]
[tex] 1 - {x}^{2} = 0 [/tex]
[tex] x_1 = 1 [/tex] [tex] x_2 = -1 [/tex]
[tex] \frac{dy}{y} = \frac{xdx}{1 - {x}^{2} } [/tex]
[tex] \int\frac{dy}{y} = \int \frac{xdx}{1 - {x}^{2} } [/tex]
[tex]ln |y | = - \frac{ln | {x}^{2} - 1| }{2} + ln |C| [/tex]
[tex]2ln |y| = ln |C| - ln | {x}^{2} - 1 | [/tex]
[tex] {y}^{2} = \frac{C}{{x}^{2}-1} [/tex]
[tex] x_1 = 1 [/tex] [tex] x_2 = -1 [/tex]