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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
8 p6 Q: I3 E) o, w>> syms a b c d e;2 n. [6 u P1 b3 \( q8 l
>> y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e')
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y =/ R- T" B8 x' o0 c$ J
; Q, R( r6 U2 C(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)), E8 @4 h! Z0 `% U, L/ T; g2 ^
3 [' i1 c) B& U" A>> a=1;b=1;c=1;d=1;e=1;%若常数已知
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3 t' W- D# m C7 b! ^& B" [>> 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 @3 [9 ~9 c4 n6 n
>> y=eval(y)
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: a7 m* A" B: O8 M2 h+ ` My =% K7 C1 {% j% [: I p3 V
: e% c$ L$ C% h6 y8 O; t# }0 j5 X 1.1932 + 0.0000i1 ~" i% l n# [' e
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。: K$ k/ ~, K, F9 r7 c( j
syms a b c d e;% ]( \$ q" E8 g1 r$ S
y=dsolve('a*D2y+b*Dy+c*y=0','y(0)=d','Dy(0)=e','x');
/ J$ R# R3 v& A5 e0 A+ J1 h5 @x=200:0.1:400;%取值范围,步长! g; ]; B; \ _9 }; Q3 R4 N( Z
a=1;b=1;c=1;d=1;e=1;%带入参数
1 { ]' x. P3 H0 Z8 ry=eval(y);
) e0 N( @( s. h6 J# `4 Gplot(x,y) |
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