The solution of the differential equation dy dx = (a e^ bx + c mx… - Vidyadip

MCQ

The solution of the differential equation $\frac{{dy}}{{dx}} = (a{e^{bx}} + c\cos mx)$ is

A
$y = \frac{{a{e^x}}}{b} + \frac{c}{m}\sin mx + k$
B
$y = a{e^x} + c\sin mx + k$
✓
$y = \frac{{a{e^{bx}}}}{b} + \frac{c}{m}\sin mx + k$
D
None of these

✓

Answer

Correct option: C.

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

c
(c) $\frac{{dy}}{{dx}} = (a{e^{bx}} + c\cos mx)$ ==> $dy = (a{e^{bx}} + c\cos mx)dx$

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

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