A) If x 1 + y + y 1 + x = 0, then prove that- dy = - (1 + x) -2 dx

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

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

If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/((1 + x)^(2))

If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y prove that (dy)/(dx) = (-1)/((1 + x)^(2))

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

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 .

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

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

If y= (x)/( x+a) , prove that x (dy)/( dx) = y(1-y) .