If `(a + bx)e^(y/x) = x`, then show that
`x^3d/dx (dy/dx) = (x dy/dx - y)^2`

If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/(dx)-y)^(2)

if e^x+e^y=e^(x+y) then show that (dy)/(dx)+e^(y-x)=0 .

If (x-y)*e^((x)/(x-y))=a , then prove that y(dy)/(dx)+x=2y .

If y =x log (x/(a+bx)) then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2 .

Find (dy)/(dx) if x^y = y^x .

If x = sint and y= sin (pt) , then show that (1-x^(2) ) (d^2y)/( dx^2) - x (dy)/( dx) + p^(2) y =0 .

IF x^y=e^(x-y) then show that (dy)/(dx)=(logx)/[log(xe)]^2 .

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .