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12.2 可分离变量的微分方程与一阶线性微分方程

12.2 可分离变量的微分方程与一阶线性微分方程

12.2 可分离变量的微分方程与一阶线性微分方程

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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)

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