Question

The solution of the differential equation

$\frac { d y } { d x } = \left( a e ^ { b x } + c \cos m x \right)$ is

• A. $y = \frac { a e ^ { x } } { b } + \frac { c } { m } \sin m x + k$
• B. $y = a e ^ { x } + c \sin m x + k$
• C. $y = \frac { a e ^ { b x } } { b } + \frac { c } { m } \sin m x + k$
• D. None of these

Answer 1

Answer: (C)

$y = \frac { a e ^ { b x } } { b } + \frac { c } { m } \sin m x + k$

Answer 2

$\frac { d y } { d x } = \left( a e ^ { b x } + c \cos m x \right)$ ⇒ $d y = \left( a e ^ { b x } + c \cos m x \right) d x$

On integrating, $y = \frac { a e ^ { b x } } { b } + \frac { c \sin ( m x ) } { m } + k$