Question

The solution of the differential equation

$\frac { d y } { d x } = e ^ { x } + \cos x + x + \tan x$ is

• A. $y = e ^ { x } + \sin x + \frac { x ^ { 2 } } { 2 } + \log \cos x + c$
• B. $y = e ^ { x } + \sin x + \frac { x ^ { 2 } } { 2 } + \log \sec x + c$
• C. $y = e ^ { x } - \sin x + \frac { x ^ { 2 } } { 2 } + \log \cos x + c$
• D. $y = e ^ { x } - \sin x + \frac { x ^ { 2 } } { 2 } + \log \sec x + c$

Answer 1

Answer: (B)

$y = e ^ { x } + \sin x + \frac { x ^ { 2 } } { 2 } + \log \sec x + c$

Answer 2

$\frac { d y } { d x } = e ^ { x } + \cos x + x + \tan x$

On integrating both sides, we get