Let $y=y(x)$ be the solution of the differential equation
$$
\begin{gathered}
\sec ^2 x d x+\left(e^{2 y} \tan ^2 x+\tan x\right) d y=0 \\
\pi \quad \pi \quad \pi \\
0
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Solution
```
${ }^3-x d x+e^3 \tan ^2 x+\tan x=0$
WUC
uly
```
( Put $\tan x=i \Rightarrow \sec ^2 x=-4$
```
$-d^2 \times 4^2+4=0+$
c
dy
- d't ${ }^3, \mathrm{E}^{-}$
$+\mathrm{E}=-\mathrm{E}$.
dy
Hijpik Hi
$+=-e^{\text {in }}$
I
1 - 4 à da
Pult $=\mathrm{ut}_{2+\infty}=\overline{-1}$
dy $d u+u=-d y$
du 3r
_ $-\mathrm{in}=\mathrm{e}$
dy
I.F. $=e-J \Delta_s=e>$
$u k-y=\int a-y \mathrm{~K} d 2 y \mathrm{~d} y$
1
$\int_{\tan x} \mathrm{KCF}=\mathrm{F}^{\circ}+\mathrm{C}$
$x=\frac{x}{4}, y=0, c=0$
$\mathrm{x}=\frac{\mathrm{T}}{6} \cdot \mathrm{y}=0 \mathrm{tr}$
$\sqrt{3} e^{-c}=e^a+0 e$
$3 \pi=\sqrt{3}$
```
$k^{3 \pi}=9$
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