按这个改一下我的MATLAB程序:R1=1.2e-3; R2=9.2e-3; Cin=1.1e6; Cwall=1.86e8; PN=8; qout=0; y=dsolve('D2y+(1/R1/Cin+1/Cwall/Cin+1/R2/Cwall)*D2y+1/R1/R2/Cin/Cwall*y=(R1+R2)/R2/Cwall*x+qout/Cwall/R2','x');
时间: 2023-12-06 07:04:23 浏览: 77
根据警告信息,我们需要使用sym对象来定义微分方程,可以按照以下方式修改你的MATLAB程序:
```
syms y(x)
R1=1.2e-3;
R2=9.2e-3;
Cin=1.1e6;
Cwall=1.86e8;
PN=8;
qout=0;
eqn = diff(y,x,2)+(1/R1/Cin+1/Cwall/Cin+1/R2/Cwall)*diff(y,x,1)+1/R1/R2/Cin/Cwall*y==(R1+R2)/R2/Cwall*x+qout/Cwall/R2;
ySol(x) = dsolve(eqn);
```
在这里,我们首先定义了符号变量y(x),然后使用sym对象来定义微分方程eqn,最后使用dsolve函数求解微分方程,并将结果保存在符号变量ySol(x)中,以便后续的操作。
相关问题
给出matlab程序,其中R1 = 1.2e-3; R2 = 9.2e-3; Cin = 1.1e6/60; Cwall = 1.86e8/60; PN = 8000; qin = 20; qout = 0; u1 = diff(u); v1 = diff(v);
根据题目给出的参数和变量,可以编写如下的Matlab程序:
```
% 定义常数
R1 = 1.2e-3;
R2 = 9.2e-3;
Cin = 1.1e6/60;
Cwall = 1.86e8/60;
PN = 8000;
qin = 20;
qout = 0;
% 定义常微分方程
syms u v
eq1 = Cin*u == PN - (u - v)/R1;
eq2 = Cwall*v == (u - v)/R1 - (v - qout)/R2;
% 求解稳态解
u_steadystate = solve(eq1, u);
v_steadystate = solve(eq2, v);
% 输出稳态解
fprintf('u_steadystate = %f\n', double(u_steadystate));
fprintf('v_steadystate = %f\n', double(v_steadystate));
% 求解u和v对时间的导数
u1 = diff(u);
v1 = diff(v);
% 定义时间t和初值条件
tspan = [0 100];
y0 = [u_steadystate, v_steadystate];
% 定义ODE函数
odefun = @(t, y) [Cin*(PN - (y(1) - y(2))/R1) - qin; ...
Cwall*((y(1) - y(2))/R1 - (y(2) - qout)/R2)];
% 求解ODE方程
[t, y] = ode45(odefun, tspan, y0);
% 绘制u和v随时间变化的图像
figure;
plot(t, y(:, 1), 'r-', t, y(:, 2), 'b--', 'LineWidth', 2);
xlabel('Time (s)');
ylabel('Value');
legend('u', 'v');
title('u and v vs. Time');
```
该程序首先求解常微分方程的稳态解,然后定义ODE函数,使用ode45函数求解ODE方程,最后绘制u和v随时间变化的图像。
syms y(x) R1 = 1.2e-3; R2 = 9.2e-3; Cin = 1.1e6; Cwall = 1.86e8; PN = 8; qout = 0; eqn = diff(y,x,2)+(1/R1/Cin+1/Cwall/Cin+1/R2/Cwall)*diff(y,x,1)+1/R1/R2/Cin/Cwall*y==(R1+R2)/R2/Cwall*x+qout/Cwall/R2; a=diff(y); cond = [eqn(0)==0, a==0]; ySol(x) = dsolve(eqn, cond);报错
在您的代码中,`eqn(0)`和`diff(y)`都不是有效的MATLAB语法。如果您想定义初始条件,请使用`y(0)`和`subs(diff(y),x,0)`。
以下是修改后的代码,应该可以求解该微分方程:
```
syms y(x) R1 = 1.2e-3; R2 = 9.2e-3; Cin = 1.1e6; Cwall = 1.86e8; PN = 8; qout = 0; eqn = diff(y,x,2)+(1/R1/Cin+1/Cwall/Cin+1/R2/Cwall)*diff(y,x,1)+1/R1/R2/Cin/Cwall*y==(R1+R2)/R2/Cwall*x+qout/Cwall/R2; a=diff(y); cond = [y(0)==0, subs(a,x,0)==0]; ySol(x) = dsolve(eqn, cond);
```
请注意,这个微分方程可能不是初值问题,因为它只给出了一个初始条件。如果您需要唯一解,请提供另一个初始条件或边界条件。
阅读全文