[英]Solve system of equations: 2 differential, 1 quadratic in matlab
Write a Matlab(or other) code for solving the system numericaly: w'(t)=dw(t)/dt;编写 Matlab(或其他)代码来求解系统数值:w'(t)=dw(t)/dt;
w'(t)=3*w(t)*y(t),
y'(t)=8*w(t)*y(t),
t^2=9+w(t)+y(t)
I don't know how to use ode45 for this as t has 2 solutions.我不知道如何为此使用 ode45,因为 t 有 2 个解决方案。
Why do you need to solve this numerically?为什么你需要用数值来解决这个问题? For a numeric solution, you would need at least an initial condition, ie
w(0), y0)
.对于数值解,您至少需要一个初始条件,即
w(0), y0)
。
Note that, by comparing the first two equations: 8w'(t) = 3y'(t)
注意,通过比较前两个方程:
8w'(t) = 3y'(t)
Then, derive the third equation to obtain:然后,推导出第三个方程,得到:
2t = w'(t)+y'(t)
This implies :这意味着 :
8*3*2t = 8*3*w'(t)+8*3*y'(t)
48t = 8*3*w'(t)+8*8*w'(t)
48t = 88*w'(t)
6t = 11*w'(t)
Thus w'(0)=0
and y'(0)=0
.因此
w'(0)=0
和y'(0)=0
。
Therefore, from the first equation: w(0)*y(0)=0
.因此,从第一个方程:
w(0)*y(0)=0
。
Because the equations are symmetric, there are two solutions as you mention.因为方程是对称的,所以你提到有两种解决方案。 Assume
w(0)=0
, then from the third equation, 'y(0)=-9'.假设
w(0)=0
,那么从第三个方程,'y(0)=-9'。 And from 6t = 11*w'(t)
we have w(t)=(6/11)t
, and y(t)=-9+(48/33)t
.从
6t = 11*w'(t)
我们有w(t)=(6/11)t
和y(t)=-9+(48/33)t
。
The other solution is y(t)=(6/11)t
, and w(t)=-9+(48/33)t
.另一个解决方案是
y(t)=(6/11)t
和w(t)=-9+(48/33)t
。
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