If `y=(x+1)^(1/2) -(x-1)^(1/2)` the value of the expression `(x^2-1)(d^2y)/(dx^2)+(xdy)/(dx-y)/4` is give by

If y=log[x+(1+x^(2))^(12)] the value of the expression ((x^(2)+1)d^(2)y)/(dx)+(xdy)/(dx) is-

If y=a[x+(x^2-1)^(1/2)]^n+b[x-(x^2-1)^(1/2)]^n the value of the expression (x^2-1)(d^2y) / dx^2+x dy / dx-n^2y is __________.

If =a[x+(x^(2)-1)^((1)/(2))]^(n)+b[x-(x^(2)-1)^((1)/(2))]^(n) the value of the expression (x^(2)-y)(d^(2)y)/(dx^(2))+x(dy)/(dx)-n^(2)y is

If y=[x+sqrt(x^2-1)]^(15)+[x-sqrt(x^2-1)]^(15) then prove that (x^2-1)(d^2y)/(dx^2)+x(dy)/(dx)-225y=0

If y=(sin^-1x)^2 , find the value of (1-x^2)(d^2y)/(dx^2)-xdy/dx+4

The solution of (y - (xdy)/dx)= 3 (1-x^(2)(dy)/(dx)) is

If y=sin(2sin^-1x) show that (1-x^2)(d^2y)/(dx^2)= xdy/dx-4y

If y=tan^-1x , prove that , (x^2+1)(d^2y)/(dx^2)+2xdy/dx=0 .

" If "2x=y^(1/3)+y^((-1)/(3))," then the value of "((x^(2)-1))/(y)(d^(2)y)/(dx^(2))+(x)/(y)(dy)/(dx)=