If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 =

1) -n^2y 2) n^2y 3) 0 4) none of these

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If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 =
1) -n^2y 2) n^2y 3) 0 4) none of these

Anuradha Sharma · Accepted Answer

y1n+y-1n=2x 1squaring we get, y2n+y-2n+2=4x2 2So
ddxy1n+y-1n=ddx2x1ny1n-1dydx-1ny-1n-1dydx=2So
y'=2ny1n-1-y-1n-1=2ny1ny-y-1ny=2nyy1n-y-1nor y1n-y-1n=2nyy' 3Again
diffrentiating we get
y''=y1n-y-1nddx2ny-2nyddxy1n-y-1ny1n-y-1n2y''=2ny1n-y-1ny'-2ny1ny1n-1+1ny-1n-1y'y2n+y-2n-2Now
putting the value from equation 1,2,3 we get, =2n2nyy'y'-2yy
y1n+y-1ny'4x2-2-2=4n2y-4xy'4x2-1So y''x2-1=n2y-xy'or
y''1-x2-xy'=-n2y

If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 = 1) -n^2y 2) n^2y 3) 0 4) none of these

If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 =

1) -n^2y 2) n^2y 3) 0 4) none of these