Question
Wed July 04, 2012 By:

if y=(tan-1x)^2 ..(tan inverse x whole squared) , p.t. ((x^2+1)^2 )y2 + 2x(x^2+1)y1=2

Expert Reply
Thu July 05, 2012
Answer : Given : y=(tan-1x)2 
To Prove : ((x2+1)2 )y2 + 2x(x2+1)y1=2
 
now,
y=(tan-1x)2
diff both sides wrt to x
=> y1 = (2 tan-1x ) / ( 1 + x2)  { d( tan -1 x) / dx = 1/ (1 + x2) }
=>( 1 + x2) y1 = 2 tan-1
diff again both sides wrt x
=> ( 1 + x2) y2 + 2x y1= 2 /( 1 + x2 )
=> ( 1 + x2)2 y2 + 2x ( 1+x2)y1= 2
hence proved
 
here y1 = dy / dx ( single differentiation)   and
    y2 = d2y / d x 2 ( double differentiation)
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