The general solution of the differential equation `(dy)/(dx)=e^(x+y)`is (A) `e^x+e^(-y)=C` (B) `e^x+e^y=C` (C) `e^(-x)+e^y=C` (D) `e^(-x)+e^(-y)=C`

Options

A. `e^(x)+e^(-y)=C`
B. `e^(x)+e^(y)=C`
C. `e^(-x)+e^(y)=C`
D. `e^(-x)+e^(-y)=C`

Explanation

Given, `(dy)/(dx)=e^(x+y)implies(dy)/(dx)=e^(x)e^(y)`
`implies e^(-y)dy=e^(x)dx`
`implies inte^(-y)dy=inte^(x)dximplies (e^(-y))/(-1)=e^(x)+A`
`implies e^(x)+e^(-y)=-Aimplies e^(x)+e^(-y)=C`, where `C=-A`