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1 e<br />
. y′<br />
+ y = .<br />
x x<br />
1<br />
x<br />
e<br />
P ( x)<br />
= , Q(<br />
x)<br />
= ,<br />
x<br />
x<br />
1<br />
⎛ x 1<br />
−∫ dx<br />
⎞<br />
⎜ e ∫ dx<br />
y = e x ⋅ + ⎟<br />
⎜∫<br />
e x dx C<br />
x<br />
⎟<br />
⎝<br />
⎠<br />
⎛<br />
x<br />
−ln x e<br />
⎞<br />
= ⎜∫<br />
ln x<br />
e ⋅ e dx + C<br />
⎟<br />
⎛<br />
x<br />
1 e<br />
=<br />
⎝ x<br />
⎠<br />
⎜∫ ⋅ x dx + C<br />
x ⎝ x<br />
= 1 ( ∫ e dx + C )<br />
x 1<br />
= ( e<br />
x + C<br />
x<br />
x<br />
).<br />
x<br />
⎞<br />
⎟<br />
⎠
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