Question

The solution of the differential equation `dy/dx = x^3 + cos4x` is ______ 

Options

• `y = x^4/4 + (sin4x)/4 + c`

• `y = x^4/4 - (sin4x)/4 + c`

• `y = x^4/4 + sin4x + c`

• `y = x^4/4 - 4sin4x + c`

Answer 1

The solution of the differential equation `dy/dx = x^3 + cos4x` is `underline(y = x^4/4 + (sin4x)/4 + c)`.

Explanation:

`dy/dx = x^3 + cos4x`

 Integrating on both sides, we get

`int dy = int(x^3 + cos 4x)dx + c`

⇒ `y = x^4/4 + (sin4x)/4 + c`