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 + e^y = C

• e^-x + e^-y = C

Answer 1

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

Explanation:

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

⇒ e^-y  dy   e^x dx

On integrating

`int` e^-y  dy = `int` e^x dx + C

⇒ -e^-y = e^x - C

∴ e^x + e^-y = C