If `y = e^(m sin^(-1)x)` then prove that `(1-x^2)y_(n+2)-(2n+1)xy_(n+1)-(n^2+m^2)y_n=0`

If y =e ^( m Cos ^(-1)x) then show that (1- x^(2)) y _(2) - xy_(1) -m^(2) y =0.

If y = e ^(Sin^(-1)x ) then (1 - x ^(2)) y _(2) - xy_(1) -y=

If y = e^(sin^ [-1] x), then (1 - x^(2))y_(2) - xy_(1) =

If y=ax^(n+1)+bx^(-n) then show that x^(2)y''=n(n+1)y .

y = sin (m Sin ^(-1)x ) implies ( 1- x ^(2)) y _(2) - xy _(1) =

If y = sin(m sin^(-1)x) , then (1-x^(2))y_(2) - xy_(1) is equal to (Here, y_(n) denotes (d^(n)y)/(dx^(n)) )

If I_(n) = int (sin nx)/(cosx)dx , prove that I_(n)=-(2)/(n-1)cos(n-1)x-I_(n-2)

If x_(n) + iy_(n) = (1 + i)^(n) then x_(n - 1) y_(n) - x_(n) y_(n- 1) =

If y = (x+ sqrt(x ^(2) -1))^(m) then (x ^(2) -1) y_(2) + xy _(1)=