If `y=Asin^2x+Bcos^2x` then prove that `sin2xy_2-2cos2xy_1=0`

If y=A sin^2x+Bcos^2x then prove that sin2x.y_(2)-2cos2x.y_(1)=0 where y_(1)=(dy)/(dx),y_(2)=(d^2y)/(dx^(2)) .

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

If y=[sin^-1 x]^2 , then prove that : (1 -x^2) y_2-xy_1 - 2 = 0 .

If y = sin(mcos^(-1)x) then prove that (1-x^(2))y_(2)-xy_(1)+m^(2)y=0 .

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

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then prove that (1-x^2)y_2-xy_(1)-4=0.

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

If y=(cos^(-1)x)^(2) , then prove that : (1-x^(2))y_(2)-xy_(1)-2=0 .

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_2-3xy_1-y=0