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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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: z: o7 P3 I* ~) w>> clear; z! ^6 |8 h% T0 Y. G
>> syms a b c d e;
3 Y; T- y8 Z h( U" V+ R+ K, T& m>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')* t$ D0 y8 p v. P9 _. `
+ K6 e3 q9 `2 [4 F1 Fy =& I0 q# r' t; O4 ?4 v
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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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4 w% S' L0 U, S>> 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 u" y9 m# w0 k( A>> y=eval(y)
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! Q0 X6 {8 U5 {3 Gy =; b7 p% ~# G, S0 ?# i; ^0 K
3 t3 I4 k' S9 F# u; u! V+ K* x 1.1932 + 0.0000i6 c" M( r5 [9 ^3 Y% _0 _
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。% U: i9 w; [+ [7 p: U6 M
syms a b c d e;
! T$ ~# k/ b* [! Iy=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');
" K. e' L0 y4 v; g: p K: |x=200:0.1:400;%取值范围,步长) g5 X( s/ s6 R8 K$ r& |$ v
a=1;b=1;c=1;d=1;e=1;%带入参数3 J- |: |& Y& s9 o7 l
y=eval(y);
# o' S* q2 g' e4 k: B5 S1 Nplot(x,y) |
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