`(dy)/(dx) +1 = e^(x+y)`

If e^(x) + e^(y) = e^(x + y) , then prove that (dy)/(dx) = (e^(x)(e^(y) - 1))/(e^(y)(e^(x) - 1)) or (dy)/(dx) + e^(y - x) = 0 .

Find the general solutions of the following differential equations. (i) (dy)/(dx) = e^(x+y) (ii) (dy)/(dx) = e^(y-x) (iii) (dy)/(dx) = (xy+y)/(yx+x) (iv) y(1+x)dx+x(1+y)dy = 0

(dy)/(dx) -y =e^(x ) " when" x=0 and y=1

(dy)/(dx)=e^(x-y)+1

Find the general solution of the following differential equation : (dy)/(dx) = (1)/(e^(-y) - x)

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

The solution of (dy)/(dx) + (1)/(x) = (e^(y))/(x^(2)) is

(dy)/(dx)=1+e^(2x-y) , given y=2, when x=2