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发表于 2014-7-14 00:28:29
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matlab 二阶微分方程
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>> clear
9 [/ ~/ A5 H( C# P>> syms a b c d e;
, t7 o4 ?: s7 f* K# ~+ L4 |>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')+ p+ \# l: m( X
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y =- z" K- {' D; `* v& \/ Z$ R0 `
( C1 J2 M: V4 z' y0 e. [8 O(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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4 |& }/ z, Z# v6 t/ | o5 B>> a=1;b=1;c=1;d=1;e=1;%若常数已知7 S% w& s: \. F6 h& U, ^
; o6 L- b$ F5 B* b$ e>> 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
, w% r7 }. Q7 R>> y=eval(y) ' A0 d, K- p; ?: {: ]
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y =
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w! W) T; P3 S- T- g! v8 Z 1.1932 + 0.0000i
, R, C+ d' u$ q0 }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。$ W; ^$ |& q% ?' k
syms a b c d e;
2 f( m+ L0 r" y" W! A6 w. Ay=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');
% b; S( J4 `/ A+ t3 _/ x& H' v6 xx=200:0.1:400;%取值范围,步长
* I4 Q( ~' y- w, a) Sa=1;b=1;c=1;d=1;e=1;%带入参数" a3 \4 Q9 `7 _( |( F& H# k z
y=eval(y);1 ~) j \9 c/ y) G
plot(x,y) |
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