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`

Explanation

Correct option is B)


``
`text { Given that, } frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} `


`Rightarrow frac{d y}{d x}=e^{x} e^{-y}+x^{2} e^{-y} `


`Rightarrow frac{d y}{d x}=frac{e^{x}+x^{2}}{e^{y}}`


`Rightarrow e^{y} d y=(e^{x}+x^{2}) d x`


``
On integrating both sides, we get


...