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

If y = cos (m sin^(-1) x), prove that (1-x^2)y_3 -3 xy_2 + ( m^2 -1) y_1=0

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 = ( cos^(-1) x)^2 , prove that (1-x^2) (d^2 y)/(dx^2) - x(dy)/(dx) - 2=0 . Hence find y_2 when x=0 .

If y= (cos^(-1) x)^2 , prove that (1-x^2) (d^2y)/(dx^2) - x(dy)/(dx) -2 =0 , Hence find y_2 when x=0 .

If e^(cot^(-1)x) Prove that (1+x^(2))y_(2) +(2x + 1)y_(1) = 0 .

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

If y= 5 cos x-3 sin x , prove that (d^(2)y)/(dx^(2))+y=0 .