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发表于 2014-7-14 00:28:29
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matlab 二阶微分方程! V1 }$ e& m( j5 L1 {( I
* T( i6 E- Z9 z" m. Y t: e>> clear
7 i$ v2 ~. c- q>> syms a b c d e;+ a! a; ^4 q9 b1 ?/ N
>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e'), b9 |$ B5 Z7 h) w& g1 L I! Z7 J% E
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y =5 Z0 ^0 |: g+ c3 y& t4 K" e
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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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1 Z( u* i' ]7 r>> a=1;b=1;c=1;d=1;e=1;%若常数已知# S2 G* A! ~' }
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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. j" j* J# R* s' p5 U0 ]
>> y=eval(y)
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& S1 W7 l+ X+ c9 [. k1 x1 E$ Gy =0 v n7 ~- F! j. ?$ W9 y4 _
# [/ r4 y6 Y' K! D$ | 1.1932 + 0.0000i
$ y7 \- X& p* l! R/ W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。! w6 c* V8 w3 O% ~+ [
syms a b c d e;
9 S4 B1 ~' x; M' V- Iy=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');
, E5 b5 z6 }( p( A3 nx=200:0.1:400;%取值范围,步长5 a9 B# \( N; K) a! W( h9 x5 _5 f
a=1;b=1;c=1;d=1;e=1;%带入参数6 {: Q0 G5 U! }9 Z+ ^6 ~
y=eval(y);$ a, x7 D3 o# n0 w2 [ h
plot(x,y) |
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