`x(dy)/(dx)-y=log x`

Solve the differential equation x(dy)/(dx)=y(log y - log x +1) .

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

Let y(x) is the solution of differential equation x(dy)/(dx)+y=x log_ex and 2y(2)=log_e 4-1 . Then y(e) is equal to (A) e^2 /2 (B) e/2 (C) e/4 (D) e^2/4

The solution of the differential equaton (dy)/(dx)=(x log x^(2)+x)/(sin y+ycos y) , is

The general solution of the differential equation, x((dy)/(dx))=y.log((y)/(x)) is

Solve (dy)/(dx)+(y)/(x)=log x.

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

If y=(x-1)log(x-1)-(x+1)log(x+1), prove : (dy)/(dx)=log((x-1)/(1+x))

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

If x^y=e^(x-y), show that (dy)/(dx)=(logx)/({log(x e)}^2)