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Please solve the question in the attachment............ .

Please solve the question in the attachment............ . 

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Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
2x = y1/n + y-1/n ----1
diff. both the sides w.r.t.  x
2 = [1/n .y1/n-1 + (-1/n).y-1/n] dy/dx
​[y1/n - y-1/n] dy/dx = 2ny
sq. both the sides,
[(y1/n - y-1/n-1)​2] (dy/dx)2 = 4n2y2
[(y1/n + y-1/n)2- 4] (dy/dx)2 = 4n.n.y.y
From 1,
[(2x)2 - 4)] (dy/dx)2 = 4n.n.y.y
[(4x2 - 4)] (dy/dx)2 = 4n2y2
(x2 - 1) (dy/dx)2 = n2y2
again diff. w.r.t. x,
2.y1.y2 (1-x2) + 2xy12 = 2y.y1n2
dividing both the sides by 2y1, we get
(1-x2)y2 + xy1=yn2
Thus option 2 is correct.

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