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

If y=cot x show that (d^(2)y)/(dx^(2))+2y(dy)/(dx)=0

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

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

If y=ae^(2x)+be^(-x), show that (d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0

If y=x^(2)e^(x),"show that "(d^(2)y)/(dx^(2))-(dy)/(dx)-2(x+1)e^(x)=0

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

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

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

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

If e^(y)(x+1)=1, show that (d^(2)y)/(dx^(2))=((dy)/(dx))^(2) If y=sin(2sin^(-1)x), show that ((1-x^(2))d^(2y))/(dx^(2))=x(dy)/(dx)-4y