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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
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>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')
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( _) x5 k- g2 e; j1 `& P3 c3 vy =; K; ]- e/ P+ C! o4 p8 O+ d# n/ j
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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)), E4 |2 j2 _8 U3 }$ @$ {0 o; ~9 l2 _9 l3 z
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>> a=1;b=1;c=1;d=1;e=1;%若常数已知6 {% S9 b: R1 q2 W; ?8 M
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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3 F o6 Z( ]8 n
>> y=eval(y)
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* l; x- Z2 L/ j! N9 g# ~' t( X2 Z7 sy =& e; ]3 a. @7 e4 P
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1.1932 + 0.0000i
' o) u) E5 Y( \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。; T# [; E$ ?8 M T" t
syms a b c d e;
% _, K5 v* A% C/ u; `7 }% s% \ u) Ty=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');! i$ j: W2 s4 A! y
x=200:0.1:400;%取值范围,步长
' j% t. [) B" @0 ?, r' [$ Za=1;b=1;c=1;d=1;e=1;%带入参数
+ L: U4 W' E0 A1 k1 m6 gy=eval(y);
: Q/ J4 ?5 P# E0 S7 R& ?2 tplot(x,y) |
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