Question

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

Options

• `2e^xy = e^{2x} + c`

• `e^xy = 2e^{2x} + c`

• `1/2e^xy = e^{2x} + c`

• `e^xy = e^{2x} + c`

Answer 1

The solution of the differential equation `dy/dx + y = e^x` is `underline(2e^xy = e^{2x} + c)`.

Explanation:

Here, P = 1 and Q = e^x

∴ I.F. = `e^{int1 dx} = e^x`

∴ solution of the given equation is

`y . e^x = inte^x . e^x dx + c_1`

⇒ `e^xy = e^{2x}/2 + c_1 ⇒ 2e^x y = e^{2x} + c`, where c = 2c₁