x^(y)+y^(x)=1

If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y then prove that y=2

If x ^(y) + y ^(x) = a ^(b) then show that (dy)/(dx) =- ((y x ^(y-1) + y^(x) log y)/( x ^(y) log x + x y ^(x -1)))

If x^y+y^x= (x+y)^(x+y) , then prove that dy/dx= ((x+y)^(x+y) [1+log(x+y)]-yx^(y-1)-y^xlogy)/(x^ylogx+xy^(x-1) -(x+y)^(x+y) [1+log(x+y)]

If x^y=y^x , then prove that (x/y)^(x/y)=(x)^((x)/(y)-1) .

The general solution of the differential equation (dy)/(dx) +x (x+y)=x (x+y) ^(3)-1 is:

The general solution of the differential equation (dy)/(dx) +x (x+y)=x (x+y) ^(3)-1 is:

Fill in the blanks If x<0,y<0,x+y+(x/y)=(1/2) and (x+y)(x/y)=-(1/2), then x=( and y)/( and y)