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Rubankumar S Grade: 10
        

if y =(arcsin x)^2 ,prove that (1-x^2)y" - xy' - y=0


where y" is second derivative of y with respect to x


        y' is first derivative of y with respect to x

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

y=(sin-1 x)2


sin-1x= y1/2 ..........1


 x=sin(y)1/2


differentiating wrt x


1 = cos(y)1/2 y' /2y1/2 or


 y'=2 (y)1/2 sec(y)1/2  ........................2


again differentiating wrt x


y'' = 2[ (y)1/2 secy1/2 tany1/2 (1/2y1/2)  + secy1/2 (1/2y1/2) ]  .....................3


multiplying 1 and 2


xy' =2y1/2 tany1/2 ...............4


solving these equations we wil get the desired result


 

6 years ago
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