[" 13.If "y=(sin^(-1)x)^(2)" ,prove that "],[qquad (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^(2)y)/(dx^(2))-x(dy)/(dx)-2=0

If y=e^(m)sin^((-1)x), prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0

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

If y=(sin^(-1)x)/(sqrt(1-x^(2))) , the prove that (1-x^(2))(d^(2)y)/(dx^(2))-3x(dy)/(dx)-y=0 .

If y=e^("mcos"^(-1)x) , prove that: (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=m^(2)y

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

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

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

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^(2)y)/(dx^(2)) -x(dy)/(dx) -2=0 . Hence find y_(2) when x=0.