Question

x''+40x-30y=0 y''-20x-20y=0 在t=0时，x=0.01，x'=0，y=0.02，y'=0．用matlab任何解出x和y阿？

我在写论文，遇到这个问题，自己也用matlab来解了一下，发现答案很奇怪，不知道是不是编程出了问题，麻烦哪位大侠帮帮忙啊～

Answer 1

>> [x,y]=dsolve('D2x+40*x-30*y=0','D2y-20*x-20*y=0','x(0)=0.01,Dx(0)=0,y(0)=0.02,Dy(0)=0')

x =

(-1/2000*15^(1/2)+1/400)*exp((-10-10*15^(1/2))^(1/2)*t)+(-1/2000*15^(1/2)+1/400)*exp(-(-10-10*15^(1/2))^(1/2)*t)+(1/2000*15^(1/2)+1/400)*exp((-10+10*15^(1/2))^(1/2)*t)+(1/2000*15^(1/2)+1/400)*exp(-(-10+10*15^(1/2))^(1/2)*t)

y =

(-1/2000*15^(1/2)+1/400)*exp((-10-10*15^(1/2))^(1/2)*t)-1/3*(-1/2000*15^(1/2)+1/400)*exp((-10-10*15^(1/2))^(1/2)*t)*15^(1/2)+(-1/2000*15^(1/2)+1/400)*exp(-(-10-10*15^(1/2))^(1/2)*t)-1/3*(-1/2000*15^(1/2)+1/400)*exp(-(-10-10*15^(1/2))^(1/2)*t)*15^(1/2)+(1/2000*15^(1/2)+1/400)*exp((-10+10*15^(1/2))^(1/2)*t)+1/3*(1/2000*15^(1/2)+1/400)*exp((-10+10*15^(1/2))^(1/2)*t)*15^(1/2)+(1/2000*15^(1/2)+1/400)*exp(-(-10+10*15^(1/2))^(1/2)*t)+1/3*(1/2000*15^(1/2)+1/400)*exp(-(-10+10*15^(1/2))^(1/2)*t)*15^(1/2)

Answer 2

才5分