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Ex 9.4, 9 - Find general solution: dy/dx = sin-1 x - Ex 9.4

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  1. Chapter 9 Class 12 Differential Equations
  2. Serial order wise
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Transcript

Ex 9.4, 9 For each of the differential equations in Exercises 1 to 10, find the general solution : 𝑑𝑦﷮𝑑𝑥﷯= sin﷮−1﷯﷮𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯= sin﷮−1﷯﷮𝑥﷯ 𝑑𝑦 = sin﷮−1﷯﷮𝑥﷯ dx Integrating both sides ﷮﷮𝑑𝑦 ﷯= ﷮﷮ sin﷮−1﷯﷮𝑥.1 𝑑𝑥﷯ ﷯ y = sin−1 x ﷮﷮1 𝑑𝑥 − ﷮﷮ 1﷮ ﷮1− 𝑥﷮2﷯﷯﷯ ﷮﷮1.𝑑𝑥 ﷯﷯﷯﷯ dx y = x 𝑠𝑖𝑛﷮−1﷯− x − ﷮﷮ 𝑥﷮ ﷮1 − 𝑥﷮2﷯﷯﷯﷯ dx Let t = 1 − x2 −2xdx = dt x dx = −𝑑𝑡﷮2﷯ Hence, our equation becomes y = x sin−1 x − ﷮﷮ −𝑑𝑡﷮2 ﷮𝑡﷯﷯﷯ y = x sin−1 x + ﷮﷮ 𝑑𝑡﷮2 ﷮𝑡﷯﷯﷯ y = x sin−1 x + 1﷮2﷯ ﷮﷮ 𝑡﷮ −1﷮2﷯﷯ 𝑑𝑡﷯ y = x sin−1 x + 1﷮2﷯ 𝑡﷮ −1﷮2﷯ + 1﷯﷮ −1﷮2﷯ + 1﷯ + C y = x sin−1 x + 1﷮2﷯ 𝑡﷮ 1﷮2﷯﷯ ﷮ 1﷮2﷯﷯﷯+𝐶 y = x sin−1 x + ﷮𝑡﷯ + C Putting back value of t y = x sin−1 x + ﷮𝟏− 𝒙﷮𝟐﷯﷯ + C

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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