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

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

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

(x-y)(1-(dy)/(dx))=e^(y), where x-y=u A) ue^u-e^u=e^(x)+c B) u^(2)=e^(x)+c C) u^(2)=(1)/(2)e^(x)+c D) u^(2)e^(x)=2x+c

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

If x^(y) = e^(x-y), (dy)/(dx) =

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

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

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

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

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