Question

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

Options

• `e^x + e^-y = c`

• `e^-x + e^-y = c`

• `e^(x + y) = c`

• `2e^(x + y) = c`

Answer 1

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

Explanation:

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

`dy = e^x . e^y dx`

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

`int e^-y dy = int e^x  dx`

`e^-y/-1 = e^x + c_1`

`-e^-y = e^x +c_1     ...[c_1 = -c]`

`c = e^x + e^y`