x(dy)/(dx)=y(log y-log x+1)

If x(dy)/(dx)=y(log_(e)y-log_(e)x+1) ,then solution of the equation is

If y=x^(y^(x)) , prove that, (dy)/(dx)=(y log y(1+x logx log y))/(x logx(1-x logy)) .

If x^(logy)=logx , prove that, (x)/(y).(dy)/(dx)=(1-logx log y)/((log x)^(2))

IF y = y (x) is the solution of the differential equation, x (dy)/(dx) = y (log_(e) y - log_(e) x + 1) , when y(1) = 2, then y(2) is equal to _______

If y log x=x-y prove that (dy)/(dx)=(log x)/((1+log x)^(2))

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

If x^(y) y^(x)=5 , then show that (dy)/(dx)= -(log y + (y)/(x))/(log x + (x)/(y))