Question

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

पर्याय

• `e^x + e^-y = c`

• `e^x + e^y = c`

• `e^-x + e^y = c`

• `e^-x + e^-y = c`

Answer 1

`e^x + e^-y = c`

Explanation:

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

∴ `dy = e^x * e^y  dx`

Dividing by `e^y`,

`e^-y  dy = e^x  dx`

Integrating, we get `inte^-y  dy = int e^x *  dx`

or `- e^-y = e^x - c = e^x + e^-y = c`