Question

The solution of $\frac { d y } { d x } = e ^ { x } ( \sin x + \cos x )$is

• A. $y = e ^ { x } ( \sin x - \cos x ) + c$
• B. $y = e ^ { x } ( \cos x - \sin x ) + c$
• C. $y = e ^ { x } \sin x + c$
• D. $y = e ^ { x } \cos x + c$

Answer 1

Answer: (C)

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

Answer 2

Given equation

$\frac { d y } { d x } = e ^ { x } ( \sin x + \cos x )$

⇒ $d y = e ^ { x } ( \sin x + \cos x ) d x$

On integrating, we get $y = e ^ { x } \sin x + c$.