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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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d i R E t<br />

i<br />

m sin<br />

+ =<br />

ω<br />

d t L L<br />

i<br />

:<br />

t =<br />

0 = 0<br />

<br />

L<br />

R<br />

E<br />

<br />

K<br />

R<br />

L<br />

− ∫ dt<br />

i (t) = ⎡ E<br />

e ⎤<br />

⎢⎣ ∫<br />

m<br />

∫ d t<br />

sinω<br />

t e d t + C<br />

L<br />

⎥⎦<br />

Em<br />

= ( Rsinω<br />

t −ω<br />

Lcosω<br />

t ) + C<br />

2 2 2<br />

R + ω L<br />

−<br />

y = e ∫ P(<br />

x)d<br />

x ⎡ ∫ P(<br />

x)d<br />

x ω LE<br />

: i<br />

⎤<br />

t=0 =<br />

⎢⎣ ∫Q<br />

0(<br />

x<br />

) e C = d2<br />

x + m<br />

C2<br />

⎥⎦<br />

2<br />

R + ω L<br />

R<br />

L<br />

e<br />

−<br />

R<br />

L<br />

t

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