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

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

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

If y={x +sqrt(x^(2)+1)}^(m) , then show that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-m^(2)y=0.

If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0 .

If y="("x+sqrt(x^(2)-1)")"^(m) , then prove that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+m^(2)y=0

Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0