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

Options

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

Answer

b

Explanation

Given differential equation is
` (dy)/(dx) = e^(y+x) +e^(y-x)`
On integrating both sides , we get
` rArr int e^(-y) dy = int (e^(x)+e^(-x))dx`
` rArr -e^(-y) = e^(x) -e^(-x) -C`
` rArr e^(-y) = e^(-x) -e^(x) +C`