[MATLAB毕业设计] 求用MATLAB求解二阶微分方程组的算法 - MATLAB爱好者论坛-LabFans.com

yfl · 2009-04-15, 11:34

>> syms x5 xu t
>> m5=1290;mu=20;k5=10^5;co=1.5*10^5;kt=2*10^5;xr=0.5*sin(8*t);
>> [x5,xu]=dsolve('m5*D2x5+k5*(x5-xu)+co*(Dx5-Dxu)=0','mu*D2xu-k5*(x5-xu)-co*(Dx5-Dxu)+kt*(xu-xr)=0')

x5 =

xr+C1*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)+C2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)+C3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)+C4*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t)

xu =

-(m5*co^2*C1*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)+m5*co^2*C2*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)+m5*co^2*C3*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)+m5*co^2*C4*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t)-co^2*kt*xr+co*mu*m5*C1*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)^3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)+co*mu*m5*C2*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)^3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)+co*mu*m5*C3*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)^3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)+co*mu*m5*C4*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)^3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t)+mu*co^2*C1*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)+mu*co^2*C2*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)+mu*co^2*C3*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)+mu*co^2*C4*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t)-m5*mu*k5*C1*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)-m5*mu*k5*C2*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)-m5*mu*k5*C3*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)-m5*mu*k5*C4*RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)^2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t)-k5^2*mu*xr-k5^2*mu*C1*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 1)*t)-k5^2*mu*C2*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 2)*t)-k5^2*mu*C3*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 3)*t)-k5^2*mu*C4*exp(RootOf(_Z^4*mu*m5+(co*mu+co*m5)*_Z^3+(m5*k5+m5*kt+mu*k5)*_Z^2+co*kt*_Z+k5*kt,index = 4)*t))/(co^2*kt+k5^2*mu)
代入数值后的解：
x5 =

1/2*sin(8*t)+C1*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)*t)+C2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)*t)+C3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)*t)+C4*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)*t)

xu =

-1473621/225010000*C1*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)^2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)*t)-1473621/225010000*C2*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)^2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)*t)-1473621/225010000*C3*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)^2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)*t)-1473621/225010000*C4*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)^2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)*t)+1/2*sin(8*t)-387/450020000*C1*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)^3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)*t)-387/450020000*C2*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)^3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)*t)-387/450020000*C3*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)^3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)*t)-387/450020000*C4*RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)^3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)*t)+1/22501*C1*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 1)*t)+1/22501*C2*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 2)*t)+1/22501*C3*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 3)*t)+1/22501*C4*exp(RootOf(129*_Z^4+982500*_Z^3+1945000*_Z^2+150000000*_Z+100000000,index = 4)*t)
其中有些符号我也不认识，因为我才大二，不知对不对，你看看，如果是对的，那么请联系我，我再帮你画图，如不对，也不要见笑，因为我也是在学习吗，呵呵。我的QQ：602561167

2009-04-15, 11:34	#2
yfl 高级会员注册日期: 2009-04-11 年龄: 38 帖子: 138 声望力: 19	回复: 求用MATLAB求解二阶微分方程组的算法 >> syms x5 xu t >> m5=1290;mu=20;k5=10^5;co=1.510^5;kt=210^5;xr=0.5sin(8t); >> [x5,xu]=dsolve('m5D2x5+k5(x5-xu)+co(Dx5-Dxu)=0','muD2xu-k5(x5-xu)-co(Dx5-Dxu)+kt(xu-xr)=0') x5 = xr+C1exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)+C2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)+C3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)+C4exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t) xu = -(m5co^2C1RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)+m5co^2C2RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)+m5co^2C3RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)+m5co^2C4RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t)-co^2ktxr+comum5C1RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)^3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)+comum5C2RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)^3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)+comum5C3RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)^3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)+comum5C4RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)^3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t)+muco^2C1RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)+muco^2C2RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)+muco^2C3RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)+muco^2C4RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t)-m5muk5C1RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)-m5muk5C2RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)-m5muk5C3RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)-m5muk5C4RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)^2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t)-k5^2muxr-k5^2muC1exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 1)t)-k5^2muC2exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 2)t)-k5^2muC3exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 3)t)-k5^2muC4exp(RootOf(_Z^4mum5+(comu+com5)_Z^3+(m5k5+m5kt+muk5)_Z^2+cokt_Z+k5kt,index = 4)t))/(co^2kt+k5^2mu) 代入数值后的解： x5 = 1/2sin(8t)+C1exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)t)+C2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)t)+C3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)t)+C4exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)t) xu = -1473621/225010000C1RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)^2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)t)-1473621/225010000C2RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)^2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)t)-1473621/225010000C3RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)^2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)t)-1473621/225010000C4RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)^2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)t)+1/2sin(8t)-387/450020000C1RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)^3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)t)-387/450020000C2RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)^3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)t)-387/450020000C3RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)^3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)t)-387/450020000C4RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)^3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)t)+1/22501C1exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 1)t)+1/22501C2exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 2)t)+1/22501C3exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 3)t)+1/22501C4exp(RootOf(129_Z^4+982500_Z^3+1945000_Z^2+150000000_Z+100000000,index = 4)*t) 其中有些符号我也不认识，因为我才大二，不知对不对，你看看，如果是对的，那么请联系我，我再帮你画图，如不对，也不要见笑，因为我也是在学习吗，呵呵。我的QQ：602561167