xy=e^((x-y))

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

If (dy)/(dx)=(xy+y)/(xy+x), then the solution of the differential equation is (A) y=xe^(x)+c(B)y=e^(x)+c(C)y=Axe^(x-y)(D)y=x+A

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).

Suppose A=(dy)/(dx) of x^(2)+y^(2)=4 at (sqrt2,sqrt2), B=(dy)/(dx) of sin y+sinx=sinx.siny at (pi,pi)andC=(dy)/(dx) of 2e^(xy)+e^(x).e^(y)-e^(x)-e^(y)=e^(xy+1) at (1,1), then (A-B-C) has the value equal to.......

Suppose A=(dy)/(dx) of x^(2)+y^(2)=4 at (sqrt2,sqrt2), B=(dy)/(dx) of sin y+sinx=sinx.siny at (pi,pi)andC=(dy)/(dx) of 2e^(xy)+e^(x).e^(y)-e^(x)-e^(y)=e^(xy+1) at (1,1), then (A-B-C) has the value equal to.......

Suppose A=(dy)/(dx) of x^(2)+y^(2)=4 at (sqrt2,sqrt2), B=(dy)/(dx) of sin y+sinx=sinx.siny at (pi,pi)andC=(dy)/(dx) of 2e^(xy)+e^(x)e^(y)-e^(x)-e^(y)=e^(xy+1) at (1,1), then (A-B-C) has the value equal to.......