if `(x-a)^2+(y-b)^2=c^2` then `{1+((dy)/(dx))^2}/{(d^2y)/(dx^2)} =?`

if (x-a)^2+(y-b)^2=c^2 then ({1+((dy)/(dx))^2})^(3/2)/{(d^2y)/(dx^2)} =?

If x^(2)+y^(2)=1 then (y'=(dy)/(dx),y''=(d^(2)y)/(dx^(2)))

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx) is equal to 4 (b) 3 (c) 1 (d) 0

If y=(sin^(-1)x)^2+(cos^(-1)x)^2 , then (1-x^2) (d^2y)/(dx^2)-x(dy)/(dx) is equal to 4 (b) 3 (c) 1 (d) 0

find the order and degree of D.E : (1) ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x) (2) sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2) (3) e^((dy)/(dx))+ (dy)/(dx) =x

if (x-a)^2+(y-b)^2=c^2 , for some c>0 prove that [1+(dy/dx)^2]^(3/2) /((d^2y)/(dx^2)) is constant independent of a and b

STATEMENT -1 : for the function y= f(x), f(x) ,({1+((dy)/dx)^(2)}^(3/2))/((d^(2)y)/(dx^(2))) = - ({1+ (dx/dy)^(2)}^(3/2))/((d^(2)x)/(dy^(2))) STATEMENT -2 : (dy)/(dx) = (1/(dx))/dy and (d^(2)y)/(dx^(2)) = d/dx (dy/(dx))