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发表于 2014-7-14 00:28:29
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matlab 二阶微分方程7 V/ `& d% y' y3 u
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>> clear
: y+ Y/ D! H4 L8 m% ~3 m>> syms a b c d e; G0 t; ]) @6 {8 L0 x- k, N5 Q
>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')
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y =
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2 S% Q' W; a1 g4 G7 b( q5 ?3 V B* t(2*a*e + b*d + d*(b^2 - 4*a*c)^(1/2))/(2*exp((t*(b - (b^2 - 4*a*c)^(1/2)))/(2*a))*(b^2 - 4*a*c)^(1/2)) - (2*a*e + b*d - d*(b^2 - 4*a*c)^(1/2))/(2*exp((t*(b + (b^2 - 4*a*c)^(1/2)))/(2*a))*(b^2 - 4*a*c)^(1/2))
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>> a=1;b=1;c=1;d=1;e=1;%若常数已知; i2 N) K0 B" ~- X
+ J7 B( U+ ]1 }! T" a) H/ l0 v$ i$ W>> t=1;%desolve中没指定自变量x,这里默认为t,带入任意一个x值. w9 Y2 { j( @& l8 @( L$ Z
>> y=eval(y)
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y =
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1.1932 + 0.0000i
- f, H; |- a s, M" U这是解方程的方法,画图也差不多,我在命令窗写的改麻烦,下面是我在editor写的。
# B4 Y# C5 J8 T8 }1 vsyms a b c d e;
1 n3 r/ Z8 W0 S1 k0 Ny=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');. f7 z- A1 A1 B. a h
x=200:0.1:400;%取值范围,步长
, {/ y" j' Q j7 ba=1;b=1;c=1;d=1;e=1;%带入参数
% ~) X" Z- N, ~9 y5 ^y=eval(y);
0 d( K) I# ~, y2 a. {+ b. L8 Aplot(x,y) |
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