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

If y= e^(a cos^(-1)x), -1 le x le 1 , show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0 .

If y = Ae^(6x) +Be^(-x) prove that (d^(2)y)/(dx^(2)) - 5 (dy)/(dx) - 6y = 0

(1+x^(2))(dy)/(dx) = 1-y

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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 .