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发表于 2014-7-14 00:28:29
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matlab 二阶微分方程( l @* h- o- w9 M
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>> clear' e# f( }9 P6 i N! F
>> syms a b c d e;* @9 t: l- O" E* Y
>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')7 C; ?0 M, h- U# ~+ ]: J
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y =/ f. |: N8 j" x' p4 ]4 |+ K
. L0 v+ j/ q" R9 X' V+ x(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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" f; Q; Z0 K5 Q0 b- ?1 A>> a=1;b=1;c=1;d=1;e=1;%若常数已知
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: S/ Q9 G4 n$ G1 i1 O* z {, l2 f>> 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
0 o3 A. r7 I' i% G>> y=eval(y) 6 J- B; N9 l; f6 t) h- f* N
4 K: v# s9 o* k! ]- Ey =0 b* a2 K! Q. y7 D' x( F
x0 ~ x, o" R* y
1.1932 + 0.0000i
( z+ b% e& ]+ o5 D% J r' M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。
$ B# T+ c' @. @3 ~syms a b c d e;
h! d! h/ X$ S8 oy=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');
7 v. I, H( q4 M7 C& Y; Jx=200:0.1:400;%取值范围,步长1 b" d2 I5 f6 Z# Q% @
a=1;b=1;c=1;d=1;e=1;%带入参数- {9 Q) _3 T* D- v, d' E0 h: u& G
y=eval(y);
9 @! e( N% O- I; [8 Splot(x,y) |
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