写出各实验MATLAB代码

以下是各个实验部分的MATLAB代码示例：

### 实验2: 微分方程解析解

% 解析解
syms y(x)
eq1 = diff(y,x) == y + 2*x;
cond1 = y(0) == 1;
sol1 = dsolve(eq1, cond1);
fplot(sol1, [0 1])
title('解析解 y'' = y + 2x')
xlabel('x')
ylabel('y')

% 数值解
[t, y] = ode23(@(t,y) y + 2*t, [0 1], 1);
hold on
plot(t, y, 'r--', 'LineWidth', 2)
legend('解析解', '数值解')
grid on

figure
syms y(x)
eq2 = diff(y, x, 2) + y*cos(x) == 0;
cond2 = [y(0) == 1, diff(y, x)(0) == 0];
sol2 = dsolve(eq2, cond2);
fplot(sol2, [0 1])
title('解析解 y'''' + ycos(x) = 0')
xlabel('x')
ylabel('y')

### 实验3: 高阶微分方程（组）

#### (1) Apollo卫星的运动轨迹

function dydt = apollo_ode(t, y)
    mu = 1 / (1 + 3.04024e-6); % 地月质量比
    r1 = norm([y(1)-mu, y(2)]);
    r2 = norm([y(1)+1-mu, y(2)]);
    dydt = [y(3); y(4); 2*y(4) + y(1) - (1-mu)*(y(1)+mu)/r1^3 - mu*(y(1)-1+mu)/r2^3; ...
            -2*y(3) + y(2) - (1-mu)*y(2)/r1^3 - mu*y(2)/r2^3];
end

[t, y] = ode45(@apollo_ode, [0 10], [0.994 0 0 -2.00158510637908]);
plot(y(:,1), y(:,2))
title('Apollo卫星的运动轨迹')
xlabel('x')
ylabel('y')
axis equal
grid on

#### (2) 天体运动轨迹

function dydt = two_body_problem(t, y)
    G = 1; % 引力常数
    M = 1; % 中心物体质量
    r = norm(y(1:2));
    F = -G * M / r^3 * y(1:2);
    dydt = [y(3:4); F];
end

[t, y] = ode45(@two_body_problem, [0 10], [1 0 0 1]);
plot(y(:,1), y(:,2))
title('天体运动轨迹')
xlabel('x')
ylabel('y')
axis equal
grid on

#### (3) 波浪能装置垂荡运动模型

% 参考优秀论文实现
% https://dxs.moe.gov.cn/zx/a/hd_sxjm_sxjmlw_2022qgdxssxjmjslwzs/221106/1820293.shtml?source=hd_sxjm_sxjmlw_2022qgdxssxjmjslwzs
% 具体实现需要根据论文提供的方程和参数进行编程

### 实验4: Hodgkin-Huxley的神经元模型

function dydt = hodgkin_huxley(t, y)
    Cm = 1; % 膜电容
    g_Na = 120; % 钠离子电导
    g_K = 36; % 钾离子电导
    g_L = 0.3; % 漏电流电导
    E_Na = 50; % 钠离子反转电位
    E_K = -77; % 钾离子反转电位
    E_L = -54.4; % 漏电流反转电位
    
    m_inf = 0.1 * (y(1) + 40) ./ (1 + exp(-(y(1) + 40) / 10));
    h_inf = 1 / (1 + exp((y(1) + 65) / 6));
    n_inf = 0.01 * (y(1) + 55) ./ (1 + exp(-(y(1) + 55) / 10));
    
    alpha_m = 0.1 * (y(1) + 40) ./ (1 - exp(-(y(1) + 40) / 10));
    beta_m = 4 * exp(-(y(1) + 65) / 18);
    alpha_h = 0.07 * exp(-(y(1) + 65) / 20);
    beta_h = 1 / (1 + exp(-(y(1) + 35) / 10));
    alpha_n = 0.01 * (y(1) + 55) ./ (1 - exp(-(y(1) + 55) / 10));
    beta_n = 0.125 * exp(-(y(1) + 65) / 80);
    
    I_Na = g_Na * y(2)^3 * y(3) * (y(1) - E_Na);
    I_K = g_K * y(4)^4 * (y(1) - E_K);
    I_L = g_L * (y(1) - E_L);
    
    dydt = [(1/Cm) * (-I_Na - I_K - I_L + 10);
            alpha_m * (1 - y(2)) - beta_m * y(2);
            alpha_h * (1 - y(3)) - beta_h * y(3);
            alpha_n * (1 - y(4)) - beta_n * y(4)];
end

ySS = [-65; 0.05; 0.6; 0.32];
for i = 1:10
    y0 = [ySS(1) + i; ySS(2:end)];
    [t, y] = ode45(@hodgkin_huxley, [0 50], y0);
    if max(y(:,1)) > 0
        plot(t, y(:,1), 'r', 'LineWidth', 2);
    else
        plot(t, y(:,1), 'k');
    end
    hold on
end
title('Hodgkin-Huxley模型的动作电位')
xlabel('时间 (ms)')
ylabel('膜电压 (mV)')
legend('未激发', '激发')
grid on

### 实验5: 迟滞微分方程

function dydt = ddefun(t, y, Z)
    ylag1 = Z(:,1);
    ylag2 = Z(:,2);
    ylag3 = Z(:,3);
    ylag4 = Z(:,4);
    ylag5 = Z(:,5);
    dydt = [ylag1(1) + y(1); ylag2(1) + y(2); ylag3(1) + y(3); ylag4(1) + y(4); ylag5(1) + y(5)];
end

function s = history(t)
    s = [exp(t+1); exp(t+0.5); sin(t+1); exp(t+1); exp(t+1)];
end

lags = [1 0.5 1 1 1];
sol = dde23(@ddefun, lags, @history, [0 1]);

t = sol.x;
y = sol.y;
plot(t, y)
title('迟滞微分方程的解')
xlabel('t')
ylabel('y')
legend('y1', 'y2', 'y3', 'y4', 'y5')
grid on

以上代码涵盖了各个实验的主要部分，可以根据具体需求进一步调整和完善。