Question

The solution of the differential equation (x + 1) sin y dy = [(x + 1 )e^x log(x + 1) + e^x]dx is ______.

Options

• `cos y = 1/(x + 1) "e"^x + "c"`

• `cos "y" + "e"^x log(x + 1) + "c" = 0`

• `cos "y" = "e"^x log (x + 1) + "c"`

• cos y = (x + 1)e^x + c

Answer 1

The solution of the differential equation (x + 1) sin y dy = [(x + 1 )e^x log(x + 1) + e^x]dx is `underline(cos "y" + "e"^x log(x + 1) + "c" = 0)`.

Explanation:

(x + 1) sin y dy = [(x + 1 )e^x log(x + 1) + e^x] dx

`=> sin "y"  "dy" = "e"^x (log (x + 1) + 1/(x + 1))`dx

Integrating on both sides, we get

- cos y = e^x log(x + 1)

cos y + e^x log(x + 1) + c = 0