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

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

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

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

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.

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 .

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

(1+x+xy^(2))(dy)/(dx)+(y+y^(3))=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 .