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-y)(d^2y) / dx^2+x dy / dx-n^2y` 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(1+x^2))^n , then show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=n^2y

IF y=A (x+sqrt(x^2-1))^n+B(x-sqrt(x^2-1))^n , Show that, (1-x^2)(d^2y)/(dx^2)-xdy/dx+n^2y=0

If y=(x+sqrt(1+x^(2)))^(n) , then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=n^(2)y .

If y=(x+sqrt(1+x^(2)))^(n), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=n^(2)y

If y=e^(msin^(-1)x) prove that (1-x^2)((d^2y)/dx^2)-x(dy)/dx=m^2y

If cos^(-1)((y)/(b))=log((x)/(n))^(n) Find the value of x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+n^(2)y

If y=sin^(-1)x ,then prove that (1-x^(2))(d^(2)y)/(dx^(2))=x(dy/dx)