The solution of dy dx = e^x ( x + x) is - Vidyadip

MCQ

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

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

✓

Answer

Correct option: C.

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

c
(c) Given equation $\frac{{dy}}{{dx}} = {e^x}(\sin x + \cos x)$

==> $dy = {e^x}(\sin x + \cos x)dx$

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

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