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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: E/ P: A3 q/ ~( a: T1 m: L
>> syms a b c d e;
/ ]* Q9 v/ J2 Y>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')
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! }5 P+ P0 Y& s) x# o% \4 _y =7 F& I% y4 u( |
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(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
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>> 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
8 ^; M( L, F0 P8 u* C# T2 N" ]+ d>> y=eval(y) / K" e4 r2 b) D
6 p- N; h! q* q. D s. J' z9 qy =9 t9 e( D# {5 e
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1.1932 + 0.0000i0 {. X# j- y$ n4 [3 V: c5 |% F
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。5 C4 P4 e' H9 D% D1 C0 ]! T
syms a b c d e;7 @, Q$ R6 Q& A9 b$ u9 n# W
y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');) C1 N; p& ~7 `' J( E+ ^; l1 V: y
x=200:0.1:400;%取值范围,步长" D2 `1 H* k4 }; E4 w: Q1 y3 N# G& {
a=1;b=1;c=1;d=1;e=1;%带入参数
. Y, s" ?) t* q0 g' d) S) J" N: ~* uy=eval(y);
5 v4 d, r! ~" h [+ {* ~plot(x,y) |
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