Solution of the differential equation dy dx + y x = x is - Vidyadip

MCQ

Solution of the differential equation $\frac{{dy}}{{dx}} + \frac{y}{x} = \sin x$ is

✓
$x(y + \cos x) = \sin x + c$
B
$x(y - \cos x) = \sin x + c$
C
$x(y \cdot \cos x) = \sin x + c$
D
$x(y - \cos x) = \cos x + c$

✓

Answer

Correct option: A.

$x(y + \cos x) = \sin x + c$

a
(a) $\frac{{dy}}{{dx}} + \frac{y}{x} = \sin x$; $I.F.$$ = {e^{\int {\frac{1}{x}dx} }} = {e^{\log x}} = x$

$yx = \int {x\sin xdx} $ ==> $yx = \int {x\sin xdx} $

==> $xy = - x\cos x + \sin x + c$ ==> $x(y + \cos x) = \sin x + c$.

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