Solve `sqrt(1+p^(2))=tan(px-y).` when `p=dy/dx`

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

Solve (x+y)^(2)(dy)/(dx)=a^(2)

Solve x^(2)p^(2)+xpy-6y^(2)=0.

Solve y=2px+y^(2)p^(3).

If y= x^(tan x) + sqrt((x^(2) + 1)/(x)) then find (dy)/(dx)

If x=e^(-t^(2)), y=tan^(-1)(2t+1) , then (dy)/(dx)=

If y= log (x + sqrt(x^(2) + a^(2))) then (dy)/(dx) = ………

if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

y= sin^(-1) [(5x + 12 sqrt(1-x^(2)))/(13)] then find (dy)/(dx)

Solve [2sqrt(x y)-x]dy+ydx=0