` xy =e^(x-y )`

Let f : R^(+) rarr R satisfies the functional equation f(xy) = e^(xy - x - y) {e^(y) f(x) + e^(x) f(y)}, AA x, y in R^(+) . If f'(1) = e, determine f(x).

Let f : R^(+) rarr R satisfies the functional equation f(xy) = e^(xy - x - y) {e^(y) f(x) + e^(x) f(y)}, AA x, y in R^(+) . If f'(1) = e, determine f(x).

Solution of x dy/dx+y=xe^x is (A) xy=e^x(x+1)+C (B) xy=e^x(x-1)+C (C) xy=e^x(1-x)+C (D) xy=e^y(y-1)+C

The solution of x (dy)/(dx) + y log y = xy e^(x) is

Find dy/dx e^(xy) + y sin x = 1