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Respected, I expect the image is clear to you. hope to get the answer soon. THANK YOU.

Respected,
I expect the image is clear to you.
hope to get the answer soon.
THANK YOU.
 

Question Image
Grade:12

1 Answers

Aditya Gupta
2081 Points
3 years ago
dear student, the ques is VERY easy. the only thing is that the calcs are a bit lengthy. apart from that the ques is elementary.
y= (x+sqrt(x^2 – 1))^15 + (x – sqrt(x^2 – 1))^15 
diff wrt x
dy/dx= y’ = 15(x+sqrt(x^2 – 1))^14*(1+x/sqrt(x^2 – 1)) + 15(x – sqrt(x^2 – 1))^14*(1 – x/sqrt(x^2 – 1))
or sqrt(x^2 – 1)*y’= 15((x+sqrt(x^2 – 1))^15 – (x – sqrt(x^2 – 1))^15)
note that we have used chain rule and other std results to diff the fn
diff again both sides wrt x
sqrt(x^2 – 1)*y” + xy’/sqrt(x^2 – 1) = 15(15(x+sqrt(x^2 – 1))^14*(1+x/sqrt(x^2 – 1)) – 15(x – sqrt(x^2 – 1))^14*(1 – x/sqrt(x^2 – 1))
multiply both sides by sqrt(x^2 – 1)
(x^2 – 1)y” + xy’ = 15(15((x+sqrt(x^2 – 1))^15 + (x – sqrt(x^2 – 1))^15)= 225y
hence, (x^2 – 1)y” + xy’ = 225y
option D
KINDLY APPROVE :))

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