Misc 6 - Find general solution: dy/dx + root 1 - y2 / 1-x2 = 0 - Miscellaneous

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Misc 6 Find the general solution of the differential equation 𝑑𝑦﷮𝑑𝑥﷯+ ﷮ 1− 𝑦﷮2﷯﷮1− 𝑥﷮2﷯﷯﷯=0 𝑑𝑦﷮𝑑𝑥﷯+ ﷮ 1 − 𝑦﷮2﷯﷮1 − 𝑥﷮2﷯﷯﷯ = 0 𝑑𝑦﷮𝑑𝑥﷯ = − ﷮ 1 + 𝑦﷮2﷯﷮1 + 𝑥﷮2﷯﷯﷯ 𝑑𝑦﷮ ﷮1 − 𝑦﷮2﷯﷯﷯= 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯﷯﷯ Integrating both sides ﷮﷮ 𝑑𝑦﷮ ﷮1 − 𝑦﷮2﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ sin−1 y = − sin−1 x + C sin−1x + sin−1 y = C

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