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x < 1, y′ − 2 y = 2,<br />
<br />
y<br />
∫ 2 d x − ∫<br />
2 d<br />
= e [ ∫ 2e<br />
d x + C1]<br />
x<br />
2 x<br />
− 2 x<br />
= e [ ∫ 2e<br />
d x + C1]<br />
2 x<br />
= C1 e − 1 ( x <<br />
1)<br />
y ( 0) = 0, C<br />
1 = 1,<br />
2 x<br />
,<br />
y = e − 1 ( x < 1)<br />
x > 1, y′ − 2 y = 0,<br />
<br />
y<br />
2d<br />
x<br />
2 x<br />
= C 2 e<br />
∫<br />
= C 2e<br />
( x ><br />
1)