(dy)/(dx)+(y)/(x)log y=(y)/(x^(2))(log y)^(2)

The general solution of the differential equation (dy)/(dx)+(y ln y)/(x)=(y)/(x^(2))(ln y)^(2) is (c being the parameter and y>0 )

The general solution of the differential equation (dy)/(dx)+(y ln y)/(x)=(y)/(x^(2))(ln y)^(2) is ( c being the parameter and y>0 )

If x^(y)=y^(x) , prove that (dy)/(dx)=((y)/(x)-log y)/((x)/(y)-log x)

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

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

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

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

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

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