Question

The solution of the equation $\frac { d y } { d x } = y \left( e ^ { x } + 1 \right)$is

• A. $y + e ^ { \left( e ^ { x } + x + c \right) } = 0$
• B. $\log y = e ^ { x } + x + c$
• C. $\log y + e ^ { x } = x + c$
• D. None of these

Answer 1

Answer: (B)

$\log y = e ^ { x } + x + c$

Answer 2

$\frac { d y } { d x } = y \left( e ^ { x } + 1 \right)$ ⇒ $\frac { d y } { y } = \left( e ^ { x } + 1 \right) d x$

Integrating both sides, we get

$\log y = e ^ { x } + x + c$ .