57. Find the particular solution of the equation $y^{\prime}+y \operatorname{tg} x=0$, if $y=2$ when $x=0$.
Solution. $1^{0} . \frac{d y}{d x}+y \tan x=0$.

$2^{0} . d y=-y \tan x d x$.
$3^{0} . \frac{d y}{y}=-\tan x d x$

$4^{0} \cdot \int \frac{d y}{y}=-\int \tan x d x ; \ln |y|=\ln |\cos x|+\ln |C|, y=C \cos x$.

$5^{0}$. When $x=0, y=2$ we have $2=C \cdot 1, C=2$, i.e., $y=2 \cos x$.