If `y=cotx` show that `(d^2y)/(dx^2)+2y(dy)/(dx)=0` .

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

x=acostheta+bsintheta and y=asintheta-bcostheta, show that y^2(d^2y)/(dx^2)-x(dy)/(dx)+y=0

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

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

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

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

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

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

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

If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .