If y=f(x) is the solution of the differential equation `x^(2)dy+xydx=dx` such that `f(e)=1/e` then `int_(1)^(e)f(x)dx` equals

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation e^(x)dx+e^(y)dy=0 is

The solution of the differential equation (dy)/(dx)-e^(x-y)=1 is

The solution of the differential equation (dy)/(dx)+1=e^(x+y) , is

The solution of the differential equation x(e^(2y)-1)dy + (x^2-1) e^y dx=0 is

Solution of the differential equation (x-y)(1-(dy)/(dx))=e^(x) is

solution of differential equation (dy)/(dx)=(x+e^(x))/(y)

If y = f (x) is the solution of difierential equation. e ^(y) ((dy)/(dx )-2)=e ^(3x) such that f(0) =0, then f (2) is equal to :

what is the solution of the differential equation (dy)/(dx)=e^(x-y) (e^(y-x) -e^(y)) ?