作业帮Mathematica 解常微分方程组问题Mathematica 输入：DSolve[{{x1'[t] == k1[t]*(x2[t] - x1[t]),y1'[t] == k1[t]*(y2[t] - y1[t]),x2'[t] == k2[t]*(x3[t] - x2[t]),y2'[t] == k2[t]*(y3[t] - y2[t]),x3'[t] == k3[t]*(x4[t] - x3[t]),y3'[t] == k3[t]*(y4[t
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 02:36:44
![Mathematica 解常微分方程组问题Mathematica 输入：DSolve[{{x1'[t] == k1[t]*(x2[t] - x1[t]),y1'[t] == k1[t]*(y2[t] - y1[t]),x2'[t] == k2[t]*(x3[t] - x2[t]),y2'[t] == k2[t]*(y3[t] - y2[t]),x3'[t] == k3[t]*(x4[t] - x3[t]),y3'[t] == k3[t]*(y4[t](/uploads/image/z/8089336-64-6.jpg?t=Mathematica+%E8%A7%A3%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E7%BB%84%E9%97%AE%E9%A2%98Mathematica+%E8%BE%93%E5%85%A5%EF%BC%9ADSolve%5B%7B%7Bx1%27%5Bt%5D+%3D%3D+k1%5Bt%5D%2A%28x2%5Bt%5D+-+x1%5Bt%5D%29%2Cy1%27%5Bt%5D+%3D%3D+k1%5Bt%5D%2A%28y2%5Bt%5D+-+y1%5Bt%5D%29%2Cx2%27%5Bt%5D+%3D%3D+k2%5Bt%5D%2A%28x3%5Bt%5D+-+x2%5Bt%5D%29%2Cy2%27%5Bt%5D+%3D%3D+k2%5Bt%5D%2A%28y3%5Bt%5D+-+y2%5Bt%5D%29%2Cx3%27%5Bt%5D+%3D%3D+k3%5Bt%5D%2A%28x4%5Bt%5D+-+x3%5Bt%5D%29%2Cy3%27%5Bt%5D+%3D%3D+k3%5Bt%5D%2A%28y4%5Bt)
Mathematica 解常微分方程组问题Mathematica 输入：DSolve[{{x1'[t] == k1[t]*(x2[t] - x1[t]),y1'[t] == k1[t]*(y2[t] - y1[t]),x2'[t] == k2[t]*(x3[t] - x2[t]),y2'[t] == k2[t]*(y3[t] - y2[t]),x3'[t] == k3[t]*(x4[t] - x3[t]),y3'[t] == k3[t]*(y4[t
Mathematica 解常微分方程组问题
Mathematica 输入：
DSolve[{{x1'[t] == k1[t]*(x2[t] - x1[t]),
y1'[t] == k1[t]*(y2[t] - y1[t]),x2'[t] == k2[t]*(x3[t] - x2[t]),
y2'[t] == k2[t]*(y3[t] - y2[t]),x3'[t] == k3[t]*(x4[t] - x3[t]),
y3'[t] == k3[t]*(y4[t] - y3[t]),x4'[t] == k4[t]*(x1[t] - x4[t]),
y4'[t] == k4[t]*(y1[t] - y4[t]),(x1'[t])^2 + (y1'[t])^2 ==
v^2,(x2'[t])^2 + (y2'[t])^2 == v^2,(x3'[t])^2 + (y3'[t])^2 ==
v^2,(x4'[t])^2 + (y4'[t])^2 == v^2},{x1[0] == 0,y1[0] == a,
x2[0] == 0,y2[0] == 0,x3[0] == a,y3[0] == 0,x4[0] == a,
y4[0] == a,k1[0] == v/a,k2[0] == v/a,k3[0] == v/a,
k4[0] == v/a}},{x1[t],y1[t],x2[t],y2[t],x3[t],y3[t],x4[t],
y4[t],k1[t],k2[t],k3[t],k4[t]},t]
输出为：
{}
请问大侠哪里出错了?
Mathematica 解常微分方程组问题Mathematica 输入：DSolve[{{x1'[t] == k1[t]*(x2[t] - x1[t]),y1'[t] == k1[t]*(y2[t] - y1[t]),x2'[t] == k2[t]*(x3[t] - x2[t]),y2'[t] == k2[t]*(y3[t] - y2[t]),x3'[t] == k3[t]*(x4[t] - x3[t]),y3'[t] == k3[t]*(y4[t
格式上的错误是,大括号有一对就可以了,不需要把初始条件和微分方程分割开来.然后,即使改了也是解不了的……要不是这个没有解析解,要不就是mathematica还不会解这个方程的解析解.（mathematica的符号计算不是万能的.）所以,这个只能用NDSolve求数值解,那样要求给出v和a的具体数值,t的定义域,然后,因为不了解你这个方程的具体背景我也只能弄到这里了…… 不过我试着赋了一些v和a的值,都不符合,所以最后还得问一句,你确认这个方程组无误吗?