If `y=sin^(-1)x/sqrt(1-x^(2))` show that `(1-x^(2))y_(2)-3xy_(1)-y=0`.

(a) If y=cos(msin^(-1)x) prove that (1-x^(2))y_(3)-3xy_(2)+(m^(2)-1)y_(1)=0 (b) Find y'' if x^(4)+y^(4)=16 .

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0 .

If y= (tan^(-1)x)^(2) , show that (x^(2)+1)^(2) y_(2)+2x(x^(2)+1)y_(1)=2 .

If y= sin^(-1)x , show that (1-x^(2)) (d^(2)y)/(dx^(2))-x(dy)/(dx)0 .

If y=e^(tan^(-1)x) , show that (1+x^(2))y''+(2x-1)y'=0

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If y = sin (m sin^(-1) x), prove that (1 - x^2)y_2 -xy_1 + m^2 y = 0